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Literature cited
Publications in Russian and Russian translations
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S. A. Aliev, “A limit theorem for branching processes with immigration,”Izv. Akad. Nauk AzSSR, Ser. Fiz.-Tekh. Mat. Nauk,6, No. 2, 43–47 (1985).
S. A. Aliev, “Convergence of Galton-Watson branching processes with several types of particles.” In:Stochastic Analysis and Its Applications, Inst. Mat. Akad. Nauk UkrSSR, 4–9, Kiev (1989).
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I. S. Badalbaev, “Limit theorems for an estimate of the direction of an eigenvector of a two-type Galton Watson process,”Dokl. Akad. Nauk UzSSR, No. 2, 3–5 (1987).
I. S. Badalbaev, “Properties of a statistical estimate for the Perron root of the mean matrix of a multi-type Galton-Watson branching process,”Izv. Akad. Nauk UzSSR, Ser. Fiz.-Mat. Nauk, No. 4, 8–14 (1987).
I. S. Badalbacv and A. N. Ganikhodzhaev, “Some generalizations of limit theorems for branching processes with decreasing immigration,”Izv. Akad. Nauk UzSSR, Ser. Fiz.-Mat. Nauk, No. 6, 3–8 (1987).
I. S. Badalbaev and A. N. Ganikhodzhaev, “A limit theorem for the Bellman-Harris branching process with immigration under the condition of nonextinction.”Izv. Akad. Nauk UzSSR, Ser. Fiz.-Mat. Nauk, No. 3, 8–14 (1989).
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S. I. Badalbaev and A. Mashrabbaev, “Asymptotic behavior of the extinction probability of branching processes with immigration.”Dokl. Akad. Nauk UzSSR, No. 1, 4–7 (1984).
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I. S. Badalbaev and A. Mashrabbaev, “On the limit distribution of a critical branching process with immigration under the condition of not hitting the zero state,”Izv. Akad. Nauk UzSSR, Ser. Fiz.-Mat. Nauk. No. 5, 3–4 (1986).
I. S. Badalbaev and A. Mashrabbaev, “Asymptotic behavior of the probability of extinction of branching processes with immigration.” In:Asymptotic Methods in Mathematical Statistics, 17–34, Fan, Tashkent (1987).
I. S. Badalbaev and A. Mukhitdinov, “On an estimate of the direction of an eigenvector of the mean matrix in a multi-type Galton-Watson process with immigration.” In:Asymptotic Methods in Probability Theory and Mathematical Statistics, 44–62, Fan, Tashkent (1988).
I. S. Badalbaev and A. Mukhitdinov, “The role of the spectrum of the eigenvalues of the mean matrix in the limit behavior of the trajectories of a multi-type branching process,”Izv. Akad. Nauk UzSSR, Ser. Fiz. Mat. Nauk, No. 2, 7–12 (1987).
I. S. Badalbaev and A. Mukhitdinov, “Limit theorems for some functionals in critical multi-type branching processes.”Teor. Veroyatn. Primen.,34, No. 4, 753–757 (1989).
I. S. Badalbaev and A. Mukhitdinov, “On the limit distributions of some functionals in multi-type branching processes,”Teor. Veroyatn. Primen.,35, No. 4, 642–654 (1990).
I. S. Badalbaev and A. Mukhitdinov,Statistical Problems of Multi-Type Branching Processes, Fan, Tashkent (1990).
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I. S. Badalbaev and I. Rakhimov, “New limit theorems for multi-type branching processes with immigration of decreasing intensity,”Izv. Akad. Nauk UzSSR, Ser. Fiz.-Mat. N auk, No. 2, 17–22 (1985).
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I. S. Badalbaev and R. M. Salakhitdinov, “Estimates of the rate of convergence in limit theorems for branching processes with decreasing immigration,”Izv. Akad. Nauk UzSSR, Ser. Fiz.-M.at. Nauk, No. 1, 3–8 (1988).
I. S. Badalbaev and R. M. Salakhitdinov, “Generalizations of limit theorems for branching processes with immigration of decreasing intensity,”Izv. Akad. Nauk UzSSR, Ser. Fiz.-Mat. Nauk, No. 1, 1–12 (1985).
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R. V. Boiko, “On the power growth of mycelium colonies in models constructed on the basis of branching processes in a varying environment.” In:Probability Methods for the Investigation of Systems with an Infinite Number of Degrees of Freedom, 17–23, Inst. Mat. Akad. Nauk UkrSSR, Kiev (1986).
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V. A. Vatutin, “Sufficient conditions for regularity of Bellman-Harris branching processes.”Teor. Veroyatn. Primen.,31, No. 1. 59–66 (1986).
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V. A. Vatutin and S. M. Sagitov, “Critical decomposable Bellman-Harris processes with two types of particles,”Tr. Mat. Inst. Akad. Nauk SSSR,177, 3–20 (1986).
V. A. Vatutin and S. M. Sagitov, “Critical decomposable Bellman-Harris process with two types of particles,”Dokl. Akad. Nauk SSSR,291, No. 5, 1040–1043 (1986).
V. A. Vatutin and S. M. Sagitov, “Critical decomposable Bellman-Harris processes with two types of particles, which are ‘far from’ Markov processes,”Mat. Zametki,43, No. 2, 276–282 (1988).
V. A. Vatutin and S. M. Sagitov, “Decomposable critical Bellman-Harris branching process with two particle types. I,”Teor. Veroyatn. Primen.,33, No. 3, 495–507 (1988).
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G. V. Vinokurov, “On a critical Galton-Watson branching process with emigration,”Teor. Veroyatn. Pnmen.,32, No. 2, 378–382 (1987).
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S. A. Grishechkin, “Investigation of queueing systems with random choice discipline by branching process methods,”Dokl. Akad. Nauk SSSR,300, No. 1, 23–26 (1988).
S. A. Grishechkin, “One-channel systems with cyclic access or with processor sharing, and branching processes,”Mat. Zametki,44, No. 4, 433–448 (1988).
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I. Rakhimov, “Uniform estimates in limit theorems for branching processes with immigration,”Izv. Akad. Nauk UzSSR, Ser. Fiz.-Mat. Nauk, No. 3, 24–29 (1984).
I. Rakhimov, “A limit theorem for multi-type age-dependent branching stochastic processes with immigration,”Izv. Akad. Nauk UzSSR, Ser. Fiz.-Mat. Nauk, No. 5, 38–40 (1984).
I. Rakhimov, “Limit distributions for the total number of particles in critical Galton-Watson processes with immigration.” In:Asymptotic Problems for Probability Distributions, 106–119, Fan, Tashkent (1984).
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I. Rakhimov, “Convergence of a sequence of branching processes with immigration to processes with continuous state space.” In:Limit Theorems for Probability Distributions, 134–148, Fan, Tashkent (1985).
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I. Rakhimov, “Asymptotic behavior of the probability of hitting a fixed state for Galton-Watson processes with decreasing immigration. I,”Izv. Akad. Nauk UzSSR, Ser. Fiz.-Mat. Nauk, No. 2, 33–38 (1986).
I. Rakhimov, “Asymptotic behavior of the probability of hitting a fixed state for Galton-Watson processes with decreasing immigration. II,”Izv. Akad. Nauk UzSSR, Ser. Fiz.-Mat. Nauk, No. 3, 38–43 (1986).
I. Rakhimov, “A limit theorem for random sums of dependent indicators and its applications in the theory of branching processes,”Teor. Veroyatn. Primen.,32, No. 2, 317–326 (1987).
I. Rakhimov, “Two limit theorems for multi-type age-dependent branching processes with immigration.” In:Asymptotic Methods of Mathematical Statistics, 97–108, Fan, Tashkent (1987).
I. Rakhimov, “Statistical estimates for parameters of a subcritical Galton-Watson process with a reflecting screen.” In:Probabilitity Models and Mathematical Statistics, 76–87, Fan, Tashkent (1987).
I. Rakhimov, “Now limit theorems for Galton-Watson processes with infinite variance,”Izv. Akad. Nauk UzSSR, Ser. Fiz.-Mat. Nauk, No. 4, 29–36 (1987).
I. Rakhimov, “Asymptotics of the probability of nonextinction of decomposable branching processes with decreasing immigration,”Izv. Akad. Nauk UzSSR, Ser. Fiz.-Mat. Nauk, No. 2, 26–28 (1988).
I. Rakhimov, “Local limit theorems for critical Galton-Watson processes with decreasing immigration,”Teor. Veroyatn. Primen.,33, No. 2, 387–392 (1988).
I. Rakhimov, “A local theorem for Galton-Watson processes with immigration in the case of a uniform limit, distribution.”Serdica,14, No. 3, 234–244 (1988).
I. Rakhimov, “A local limit theorem for Galton-Watson processes with slowly decreasing immigration.” In:Asymptotic Methods in Probability Theory and Mathematical Statistics, 121–136, Fan, Tashkent (1988).
I. Rakhimov, “Asymptotic behavior of families of particles in branching stochastic processes,”Dokl. Akad. Nauk SSSR,305, No. 3, 540–542 (1989).
I. Rakhimov, “Branching stochastic processes with generalized immigration,”Izv. Akad. Nauk UzSSR, Ser. Fiz.-Mat. Nauk, No. 2, 35–40 (1989).
I. Rakhimov, “Asymptotic behavior of families of particles in branching stochastic processes.” In:Functionals of Random Processes and Statistical Inferences, 58–71, Fan, Tashkent (1989).
I. Rakhimov and S. V. Kaverin, “A class of limit distributions of critical branching processes with decreasing immigration depending on the state,”Dokl. Akad. Nauk UzSSR, No. 1, 4–6 (1986).
I. Rakhimov and S. V. Kaverin, “A method for proving limit theorems for branching processes with state-dependent immigration.” In:Probability Models and Mathematical Statistics, 61–76, Fan, Tashkent (1987).
I. Rakhimov and S. Kurbanov, “Branching processes with inhomogeneous migration and infinite variance.” In:Functionals of Random Processes and Statistical Inferences, 71–85, Fan, Tashkent (1989).
I. Rakhimov and R. M. Salakhitdinov, “Some generalizations of limit theorems for Galton-Watson processes with infinite variance and decreasing immigration,”Izv. Akad. Nauk UzSSR, Ser. Fiz.-Mat. Nauk, No. 3, 25–30 (1987).
Y. N. Reshetnyak, “A class of branching processes with interaction of particles.” In:Analytic Methods in Reliability Theory, 106–114., Inst. Mat. Akad. Na.uk UkrSSR, Kiev (1985).
Yu. M. Ryzhov and A. Y. Skorokhod, “Homogeneous branching processes with a. finite number of types and with continuously varying mass,”Teor. Veroyatn. Primen.,15, No. 4, 722–726 (1970).
S. M. Sagitov, “The probability of a critical branching process with immigration hitting zero,”Izv. Akad. Nauk KazSSR, Ser. Fiz.-Mat. Nauk, No. 5, 63–65 (1982).
S. M. Sagitov, “Limit theorem for a. critical branching process of the general type,”Mat. Zametki,34, No. 3, 453–461 (1983).
S. M. Sagitov, “Reduced critical Bellman-Harris branching process with several types of particles,”Teor. Veroyatn. Primen.,30, No. 4, 737–749 (1985).
S. M. Sagitov, “Limit behavior of general branching processes,”Mat. Zametki,39, No. 1, 144–155 (1986).
S. M. Sagitov, “On a critical branching process with immigration hitting zero.” In:Theoretical and Applied Problems of Mathematical Modeling, 5–11, Nauka KazSSR, Alma-Ata (1988).
S. M. Sagitov, “A branching process under the conditions of extinction in the distant future,”Izv. Akad. Nauk KazSSR, Ser. Fiz.-Mat. Nauk, No. 3, 37–38 (1986).
S. M. Sagitov, “Multi-dimensional limit theorems for a branching process with one type of particles,”Mat. Zametki,42, No. 1, 157–165 (1987).
S. M. Sagitov, “A criterion for the existence of a limit for the average number of particles in a critical branching process,”Izv. Akad. Nauk KazSSR, Ser. Fiz.-Mat. Nauk, No. 3, 33–40 (1988).
S. M. Sagitov, “Limit behavior of reduced critical branching processes,”Dokl. Akad. Nauk SSSR,303, No. 1, 47–49 (1988).
S. M. Sagitov, “A new limit theorem for reduced critical branching processes.”Izv. Akad. Nauk KazSSR, Ser. Fiz.-Mat. Nauk, No. 3, 33–36 (1989).
S. M. Sagitov, “A multidimensional critical branching process generated by a large number of particles of one type.”Teor. Veroyatn. Primen.,35, No. 1, 98–109 (1990).
R. M. Salakhitdinov, “An estimate for the rate of convergence in a limit theorem for a critical process with immigration,”Izv. Akad. Nauk UzSSR, Ser. Fiz.-Mat. Nauk, No. 5, 15–18 (1986).
B. A. Sevastyanov, “Theory of Branching Processes.” In:Itogi Nauki i Tekhmki, Ser. Teor. Veroyatn. Mat. Statist. Teor. Kibern., 5–46, VINITI (1968).
B. A. Sevastyanov, “Branching processes bounded from below.”Dokl. Akad. Nauk SSSR,238, No. 4, 811–813 (1978).
B. A. Sevastyanov, “Branching processes with particle interaction.” In:Abstracts of 3th World Vilnius Conf. on Probab. Theory and Math. Statist., 139–140, Vilnius (1981).
B. A. Sevastyanov, “Investigation of branching processes at the Moscow State University probability chair.”Teor. Veroyatn. Pnmen.,34, No. 1, 231–236 (1989).
B. A. Sevastyanov and A. M. Zubkov, “Controlled branching processes,”Teor. Veroyatn. Primen.,19, No. 1, 15–25 (1974).
B. A. Sevastyanov and A. V. Kalinkin, “Branching stochastic processes with particle interaction,”Dokl. Akad. Nauk SSSR,264, No. 2, 306–308 (1982).
E. V. Sernova, “Transition phenomena in reduced Bellman-Harris branching processes.” In:Stochastic Processes and Their Applications, 69–73. Moscow (1989).
A. V. Skorokhod, “Systems of interacting multiplying particles.”Tr. Tbiliss. Mat. Inst. Akad. Nauk GrSSR,92, 46–55 (1989).
D. D. Scott, “Asymptotic result for a Galton-Watson process without constraints for a supercritical case.” In:Proc. of the 1st World Congress of the Bernoulli Society, Issue I. 149–152, (Tashkent, 1986), VNU. Sci. Press, Utrecht (1987).
Yasin Makhmud Takha, “Transition phenomena for branching migration processes,”Dokl. Akad. Nauk SSSR, No. 7, 6–8 (1989).
V. A. Topchii, “Asymptotic behavior of the probability of nonextinction of critical general branching processes without the second moment in the number of descendants,”Tr. Mat. Inst. SO Akad. Nauk SSSR, No. 3, 181–197 (1984).
V. A. Topchii, “Conditions of validity of Holte's theorem for the nonextinction probability of general critical branching processes.” In:Markov Stochastic Processes and Their Applications in Queueing Theory, 22–24, Saratov (1985).
V. A. Topchii, “Properties of the probability of nonextinction of general critical branching processes under weak constraints,”Sib. Mat. Zh.,28, No. 5, 178–192 (1987).
V. A. Topchii, “Generalization of results for the nonextinction probability of general branching processes.” In:Stochastic Models and Inform. Systems, 143–179, Novosibirsk (1987).
V. A. Topchii, “Moderate deviations for the total number of particles in critical branching processes,”Teor. Veroyatn. Primen.,33, No. 2, 406–409 (1988).
V. A. Topchii, “Properties of the total number of particles on degenerate trajectories of branching processes,”Sib. Mat. Zh.,29, No. 6, 135–143 (1988).
V. A. Topchii, “Limit theorems for critical general branching processes with long-living particles.” In:Stochastic and Deterministic Models of Complex Systems, 114–153, Vychisl. Tsentr. SO Akad. Nauk SSSR., Novosibirsk (1988).
W. Feller,An Introduction to Probability Theory and Its Applications,2, Mir Publ., Moscow [Russian translation] (1984).
Sh. K. Formanov and S. V. Kaverin, “Local limit theorems for a critical Galton-Watson process with migration,”Dokl. Akad. Nauk SSSR. Ser. Fiz.-Mat. Nauk, No. 10, 5–7 (1984).
Sh. K. Formanov and S. V. Kaverin, “Markov branching process with emigration. I,”Izv. Akad. Nauk UzSSR, Ser. Fiz.-Mat. Nauk, No. 5, 23–28 (1986).
Sh. K. Formanov and S. V. Kaverin, “Markov branching process with emigration. II,”Izv. Akad. Nauk UzSSR, Ser. Fiz.-Mat. Nauk, No. 3, 36–41 (1987).
Sh. K. Formanov and S. V. Kaverin, “Branching processes withn types of particles and with migration.” In:Probability Models and Mathematical Statistics, 147–154, Fan, Tashkent (1987).
Sh. K. Formanov and Yasin Mukhmud Takha, “Limit theorems for life periods of critical Galton-Watson branching processes with migration,”Izv. Akad. Nauk UzSSR, Ser. Fiz.-Mat. Nauk, No. 1, 40–44 (1989).
T. A. Formanova, “Limit theorems for critical branching processes with state-dependent immigration. I.”Izv. Akad. Nauk UzSSR, Ser. Fiz.-Mat. N auk, No. 6, 24–29 (1984).
T. A. Formanova, “Limit theorems for critical branching processes with state-dependent immigration. II,”Izv. Akad. Nauk UzSSR, Ser. Fiz.-Mat. Nauk, No. 3, 36–41 (1985).
T. A. Formanova, “Limit theorems for critical branching processes with immigration depending on several states.” In:Mathematical Analysis and Probability Theory, 64–74, Tashkent State Univ., Tashkent (1985).
T. A. Formanova, “Asymptotic properties of branching random processes with state-dependent immigration,” In:Mathematical Analysis and Probability Theory, Manuscript, Dep. VINITI, No. 4956-B (1986).
R. H. Khairullin, “On the statistics of Galton-Watson processes with several types of particles.” In:Investigations in Applied Mathematics, No. 16, 81–97, Kazan (1989).
L. V. Khan, “Limit theorems for a Galton-Watson branching process with migration,”Sib. Mat. Zh.,21. No. 2. 183–194 (1980).
L. V. Khan, “Estimates of the rate of convergence in limit theorems for a branching migration process.” Manuscript, Dep. VINITI, No. 1222-81 (1981).
L. V. Khan, “Asymptotic behavior of a branching process with state-dependent immigration.” In:Functional Analysis, Differential Equations and Their Applications, 60–63, Alma-Ata (1987).
L. V. Khan, “Asymptotic behavior of a supercritical branching migration process.” Manuscript, Dep. VINITI, No. 2355-Ka88 (1988).
V. I. Sherstnev, “Asymptotics of the probability of branching processes with immigration and several types of particles hitting zero.” In:Probability Theory of Random Processes and Functional Analysis, 84–86, Moscow (1985).
V. I. Sherstnev, “Transition phenomena for final probabilities of branching processes,”Teor. Veroyatn. Primen.,31 No. 1, 111–117 (1986).
V. M. Shurenkov, “Limit theorems for branching processes with immigration controlled by a finite Markov chain,”Dokl. Akad. Nauk SSSR,207, No. 3, 554–556 (1972).
V. M. Shurenkov, “Some limit theorems for branching vector processes with continuous state space,”Dokl. Akad. Nauk SSSR,207, No. 2, 304–305 (1972).
V. M. Shurenkov, “Note on asymptotic behavior of branching vector processes with continuous state space.” In:Teor. Veroyatn. Mat. Statist., No. 8, 169–172, Kiev (1973).
V. M. Shurenkov, “Some limit theorems for branching processes with continuous state space.” In:Teor. Veroyatn. Mat. Statist., No. 9, 167–172, Kiev (1973).
A. P. Yurachkovskii, “Diffusion approximation of inhomogeneous branching processes that are asymptotically critical in a scheme of series.” Manuscript, Dep. VINITI, No. 1036Yk-85 (1985).
A. P. Yurachkovskii, “Convergence of inhomogeneous branching processes that are asymptotically critical in a scheme of series to processes of diffusion type.” In:Teor. Veroyatn. Mat. Statist., No. 36, 127–135, Kiev (1987).
A. L. Yakymiv, “Two limit theorems for critical Bellman-Harris branching processes,”Mat. Zametki,36, No. 1, 109–116 (1984).
A. L. Yakymiv, “Asymptotic properties of subcritical and supercritical reduced branching processes,”Teor. Veroyatn. Primen.,30, No. 1, 183–188 (1985).
A. L. Yakymiv, “Reduced branching processes with several particle types.” In:Probability Processes and Their Applications, 24–31, Moscow (1984).
A. L. Yakymiv, “Asymptotics of the probability of nonextinction of critical Bellman-Harris branching processes,”Tr. Mat. Inst. Akad. Nauk SSSR,177, 177–205 (1986).
N. M. Yanev, “Conditions for degeneracy of ϕ-branching processes with random ϕ,”Teor. Veroyatn. Primen.,20, No. 2, 433–440 (1975).
N. M. Yanev, “Controlled branching processes in a random environment,”Math. Balkan., No. 7, 137–156 (1977).
N. M. Yanev, “Branching stochastic structures.” In:Mathematics and Mathematical Education. Proc. 14th Conf. of Bulgar. Math. Union, (Sunny Beach, 1986), 171–184, Bulgar. Akad. Nauk. Sofia: (1985).
N. M. Yanev, “Limit theorems for estimates of individual characteristics in a Galton-Watson process,”Serdica,12, No. 2, 134–142 (1986).
N. M. Yanev, “Estimates of variance in a subcritical branching process with immigration,”Annuaire Univ. Sofia Fac. Math. Mec., (1976/77),71, No. 2, 39–44 (1986).
N. M. Yanev, V. A. Vatutin, and K. V. Mitov, “Critical migration branching processes with an absorbing barrier at zero.” In:Mathematics and Mathematical Education. Proc. 15th Conf. of Bulgar. Math. Union (Sunny Beach, 1986), 511–517, Bulgar. Akad. Nauk, Sofia (1986).
N. M. Yanev and K. Mitov, “Controlled branching processes with infinite expectation.” In:Mathematics and Mathematical Education. Proc. 9th Conf. of Bulgar. Math. Union, 182–186, Bulgar. Akad. Na.uk, Sofia. (1980).
N. M. Yanev and S. St. Chukova, “Limit theorems for estimates of variances in a branching process with immigration,”Serdica,12, No. 2, 143–153 (1986).
Publications in other languages
S. R. Adke, “A birth, death and migration process,”J. Appl. Probab.,6, No. 3, 687–691 (1969).
A. Agresti, “Bounds on the extinction time distribution of a. branching processes,”J. Appl. Probab.,6, No. 2, 332–335 (1974).
A. Agresti, “On the extinction times of varying and random environment branching processes,”J. Appl. Probab.,12, No. 1, 39–46 (1975).
A. A. Alzaid. C. R. Rao, and D. N. Shanbhag, “An extinction of Spitzer's integral representation theorem with an application,”Ann. Probab.,15, No. 3, 1210–1216 (1987).
N. Arató, “On the speed of convergence for critical Galton-Watson processes,”Stud. Sci. Math. Hung.,24, No. 2–3, 269–275 (1989).
S. Asmussen and H. Hering, “Strong limit theorems for general supercritical branching processes with applications to branching diffusions,”Z. Wahrschein. Verw. Geb.,36, No. 3, 195–242 (1977).
S. Asmussen and N. Kaplan, “Branching random walks. I,”Stochast. Process. Appl.,4, No. 1, 1–13 (1976).
K. B. Athreya, “Discounted branching random walks,”Adv. Appl. Probab.,17, No. 1, 53–66 (1985).
K. B. Athreya, “On the maximum sequence in a critical branching process,”Ann. Probab.,16, No. 2. 502–507 (1988).
K. B. Athreya. and N. Kaplan, “Limit theorems for a branching process with disasters,”J. Appl. Probab.,13, No. 3, 466–475 (1976).
K. B. Athreya and S. Karlin, “Branching processes with random environments.”Bull. Amer. Math. Soc.,76, No. 4, 865–870 (1970).
K. B. Athreya and S. Karlin, “On branching processes with random environments, I. Extinction probabilities,”Ann. Math. Stat.,42, No. 5, 1499–1520 (1971).
K. B. Athreya and S. Karlin, “Branching processes with random environments, II. Limit theorems,”Ann. Math. Stat.,42, No. 6, 1843–1858 (1971).
K. B. Athreya and P. Ney, “Limit theorems for the means of branching random walks.” In:Trans. 6th Prague Conf. Inform. Theory, Statist. Decis. Fund., Random Proces., 63–72, Prague, 1971, Prague (1973).
J. H. Bagley, “The existence of moments of the conditioned limit of the subcritical Grump-Mode-Jagers branching process,”Stochast. Process. Appl.,20, No. 2, 333–341 (1985).
J. H. Bagley, “On the asymptotic properties of a supercritical bisexual branching process,”J. Appl. Probab.,23, No. 3, 820–826 (1986).
J. H. Bagley, “On the almost sure convergence of controlled branching processes,”J. Appl. Probab.,23, No. 3, 827–831 (1986).
A. D. Barbour, “Second order limit theorems for the Markov branching process in random environments,”Stochast. Process. Appl.,4, No. 1, 33–40 (1976).
N. Becker, “Estimation for discrete time branching processes with application to epidemics,”Biometrics,33, No. 3, 515–522 (1977).
M. C. Bhattacharjee, “The time to extinction of branching processes and log-convexity: I,”Prob. Eng. Inf. Sci.,I, 265–278 (1987).
J. D. Biggins, “Martingale convergence in the branching random walk,”J. Appl. Probab.,14, No. 1, 25–37 (1977).
J. D. Biggins, “Chernoff's theorem in the branching random walk,”J. Appl. Probab.,14, No. 3, 630 -636 (1977).
I. D. Biggins, “The asymptotic shape of the branching random walk.”Adv. Appl. Probab.,10, No. L 62–84 (1978).
J. D. Biggins, “Growth rates in the branching random walk,”Z. Wahrschein. Verw. Geb.,48, No. 1, 17–34 (1979).
J. D. Biggins, “Spatial spread in branching processes,”Led. Notes Biomath.,38, 57–67 (1980).
J. D. Biggins, “Limiting point processes in the branching random walk.”Z. Wahrschein. Verw. Geb.,55, No. 3, 297–303 (1987).
J. D. Biggins and T. Götz, “Expected population size in the generation-dependent branching process,”J. Appl. Probab. 24, No. 2, 304–314 (1987).
J. D. Biggins and D. R. Grey, “Continuity of limit random variables in the branching random walk.”J. Appl. Probab.,16, No. 4, 740–749 (1979).
N. H. Bingham, “Continuous branching processes and spectral positivity,”Stochast. Process. Appl.,4, No. 3, 217–242 (1976).
N. H. Bingham, “On the limit of a supercritical branching process,”J. Appl Probab.,25 A, 215–228 (1988).
N. H. Bingham, “Tauberian theorems in probability theory,”Led. Notes Math.,1379, 6–20 (1989).
M. D. Bramson, “Maximal displacement of branching Brownian motion,”Commun, Pure Appl. Math.,31, No. 5, 531–581 (1978).
AI. D. Bramson, “Minimal displacement of branching random walk,”Z. Wahrschein. Verw. Geb.,45, No. 2, 89–108 (1978).
P. Broberg, “A note on the extinction probability of branching populations,”Scand. J. Statist. Theory Appl.,14, No. 2, 125–129 (1987).
P. Broberg, “Critical branching process populations with reproductive sibling correlations,”Stochast. Process. Appl.,30, No. 1, 133–147 (1988).
F. T. Bruss, “Branching processes with random absorbing processes,”J. Appl. Probab.,15, No. 1, 54–64 (1978).
F. T. Bruss, “A counterpart of the Borel-Cantelli lemma,”J. Appl. Probab.,17, No. 4, 1094–1101 (1980).
F. T. Bruss, “A note on extinction criteria for bisexual Galton-Watson processes,”J. Appl. Probab.,21, No. 4, 915–919 (1984).
P. G. Buckholtz, J. M. Hartwick, K. Nanthi, and M. T. Wasan, “Some results on first order stochastic models and estimation for diffusion approximation of the multi-type Galton-Watson process.”Stochast. Anal. Appl.,1, No. 2, 163–195 (1983).
W. J. Bühler and P. S. Puri, “The linear birth and death process under the influence of independently occurring disasters,”Probab. Theory Relat. Fields,83, No. 1–2, 59–66 (1989).
M. L. Carvalho and D. Muller, “Asymptotic bilateral tests for branching processes,”Scand. J. Statist. Theory Appl.,11, No. 1, 39–44 (1984).
L. L. Cavalli-Sforza and A. W. F. Edwards, “Estimation procedures for evolutionary branching processes,”Bull. Internat. Statist. Inst.,41, No. 2, 803–807 (1965).
K. S. Chandra and P. Koteeswaran, “Influence on superimposed subcritical Galton-Watson process with immigration,”Ann. Inst. Statist. Math.,38, No. 2, 311–313 (1986).
B. Chauvin, “Arbres et processus de Bellman-Harris,”Ann. Inst. H. Poincare. Probab. Statist.,22, No. 2, 209–232 (1986).
B. Chauvin, “Sur la proprieté de branchement.”Ann. Inst. H. Poincare. Probab, Statist.,22, No. 2, 233–236 (1986).
B. Chauvin and A. Rouault, “Etude de l'équation KKP et du branchement, brownien en zones souscritique et critique,”C. r. Acad. Sci., Ser. I,304, No. 1, 19–32 (1987).
Y. S. Chow and K. F. Yu, “Some limit theorems for a subcritical branching process with immigration,”J. Appl. Probab.,21, No. 1, 50–57 (1984).
J. D. Church, “On infinite composition of products of probability generating functions,”Z. Wahrschein. Verw. Geb.,19, No. 3, 243–256 (1971).
P. Clifford, “On the age structure of cell-size-dependent branching processes.” In:Trans. 7th Prague Conf. Inform. Theory, Statist. Decis. Funct., Random Process. and 1974 Eur. Meet, Statist., Prague, 1974,A, 97–101, Prague (1977).
P. Clifford and A Sudbury, “The linear cell-size-dependent branching process.”,J. Appl. Probab.,9, No. 4, 687–696 (1972).
P. Clifford and A. Sudbury, “Cell-size-dependent branching processes.” In:Progr. Statist.,I, 153–156. Amsterdam-London (1974).
J. Coffey and D. Tanny, “A necessary and sufficient condition for noncertain extinction of a branching process in a random environment (BR BPRE),”Stochast. Process. Appl.,16, No. 2, 189–197 (1984).
H. Cohn, “A martingale approach to supercritical (CMJ) branching processes,”Ann. Probab.,13, No. 4, 1179–1191 (1985).
H. Cohn, “Multi-type finite mean supercritical age-dependent branching processes,”J. Appl. Probab.,26, No. 2, 398–403 (1989).
H. Cohn, “On the growth of the multi-type supercritical branching process in a random environment,”Ann. Probab.,17, No. 3, 1118–1123 (1989).
H. Cohn and H. Hering, “Inhomogeneous Markov branching processes: supercritical case,”Stochast. Process. Appl.,14, No. 1, 79–91 (1983).
H. Cohn and F. Klebaner, “Geometric rate of growth in Markov chains with applications to population-size-dependent models with dependent offspring,”Stochast. Anal. Appl.,4, No. 3, 283–307 (1986).
H. E. Conner, “Asymptotic behavior of averaging-processes for a branching process of restricted Brownian particles,”J. Math. Anal. Appl.,20, No. 3, 464–479 (1967).
R. Cowan, “Branching process results in terms of moments of the generation-time distribution,”Biometrics,41, No. 3, 681–689 (1985).
K. S. Crump and C. J. Mode, “An age-dependent branching process with correlations among sister cells,”J. Appl. Probab.,6, No. 1, 205–210 (1969).
D. J. Daley, “Extinction conditions for certain bisexual Galton-Watson branching processes,”Z. Wahrschein. Verw. Geb.,9, No. 4, 315–322 (1968).
D. J. Daley, D. M. Hull, and J. M. Taylor, “Bisexual Galton-Watson branching processes with super-critical superadditive mating functions,”J. Appl. Probab.,23, No. 3, 585–600 (1986).
D. A. Dawson and E. A. Perkins, “Historical processes,”Mem. Amer. Math. Soc.,93, No. 454. 179 (1991).
F. M. Dekking, “Subcritical branching processes in a two-state random environment, and a percolation problem on trees,”J. Appl. Probab.,24, No. 4, 798–808 (1987).
F. M. Dekking, “On the survival probability of a branching process in a finite state i.i.d. environment,”Stochast. Process. Appl.,27, No. 1, 151–157 (1987).
S. R. Deshmukh, “Maximum likelihood estimation for branching migration process,”Commun. Statist: Theory Meth.,13, No. 14, 1769–1780 (1984).
J. P. Dion and W. W. Esty, “Estimation problems in branching processes with random environments.”Ann. Staust.,7, No. 3, 680–685 (1979).
P. Dittrich, “A boundary process in random environment,” Prepr. Akad. Wiss. DDR, Karl-Weier-strass Inst. Math., No. 24, 1–12 (1988).
R. A. Doney, “A note on some results of Schuh,”J. Appl. Probab.,21, No. 1, 192–196 (1984).
S. D. Durham, “An optimal branching migration process,”J. Appl. Probab.,12, No. 3, 569–573 (1975).
R. Durrentt, “Genealogy of critical branching processes,”Stochast. Process. Appl.,8, No. 1, 101–116 (1978).
R. Durrett, “Maxima of branching random walks vs. independent random walks,”Stochast. Process. Appl.,9, No. 2, 117–135 (1979).
R. Durrett, “Maxima of branching random walks,”Z. Wahrschein. Verw. Geb.,62, No. 2, 165–170 (1983).
M. Dwass, “Branching processes in simple random walk,”Proc. Amer. Math. Soc.,51, No. 2, 270–274 (1975).
L. Edler, “Strict supercritical generation-dependent Grump-Mode-Jagers branching processes,”Adv. Appl. Probab. 10, No. 4. 744–763 (1978).
L. Edler, “The extinction of generations in generation-dependent Bellman-Harris branching processes with exponential lifespan.” In:Trans. 8th Prague Conf. Inform. Theory, Statist. Decis. Fund., Random Process.,A, 171–185, Prague (1978).
A. W. F. Edwards, “Estimation of the branch points of a branching diffusion process,”J. Roy. Statist. Soc.,B32, No. 2, 155–164 (1970).
K. Enderle and H. Hering, “Ratio limit theorems for branching Ornstein-Uhlenbeck processes,”Stochast. Process. Appl.,13, No. 1, 75–85 (1982).
K. B. Erickson, “Rate of expansion of an inhomogemeous branching process of Brownian particles,”Z. Wahrschein. Verw. Geb.,66, No. 1, 129–140 (1984).
I. Eshel, “On the survival probability of a slightly advantageous mutant gene in a multi-type population: A multidimensional branching process model,”J. Math. Biol.,19, No. 2, 201–209 (1984).
D. W. Fairweather and I. N. Shimi, “An immigration and fragmentation stochastic process,”Math. Biosci.,9, No. 1, 93–104 (1970).
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Translated from Itogi Nauki i Tekhniki, Seriya Sovremennaya Matematika i Ee Prilozheniya. Tematicheskie Obzory. Vol. 2, Teoriya Veroyatnostei i Matematicheskaya Statistika — 1, 1993.
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Vatutin, V.A., Zubkov, A.M. Branching processes. II. J Math Sci 67, 3407–3485 (1993). https://doi.org/10.1007/BF01096272
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DOI: https://doi.org/10.1007/BF01096272