Bulletin of the American Mathematical Society

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Book Information:

Authors: L. C. G. Rogers and D. Williams
Title: Diffusions, Markov processes, and martingales, Volume One: Foundations, Second Edition
Additional book information: John Wiley & Sons, Chichester, West Sussex, England, 1994, xx + 386 pp., ISBN 0-471-95061-0, $79.95$

1.

Désiré André, Solution directe du problème résolu par M. Bertrand, C. R. Acad. Sci. Paris 105 (1887), 436-437.

Kai Lai Chung, Probabilistic approach in potential theory to the equilibrium problem, Ann. Inst. Fourier (Grenoble) 23 (1973), no. 3, 313–322. MR 391277

Kai Lai Chung, Lectures from Markov processes to Brownian motion, Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], vol. 249, Springer-Verlag, New York-Berlin, 1982. MR 648601

Tadasi Nakayama, On Frobeniusean algebras. I, Ann. of Math. (2) 40 (1939), 611–633. MR 16, DOI 10.2307/1968946

J. L. Doob, Classical potential theory and its probabilistic counterpart, Grundlehren der mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], vol. 262, Springer-Verlag, New York, 1984. MR 731258, DOI 10.1007/978-1-4612-5208-5

Donald A. Dawson, Measure-valued Markov processes, École d’Été de Probabilités de Saint-Flour XXI—1991, Lecture Notes in Math., vol. 1541, Springer, Berlin, 1993, pp. 1–260. MR 1242575, DOI 10.1007/BFb0084190

Eugene B. Dynkin, An introduction to branching measure-valued processes, CRM Monograph Series, vol. 6, American Mathematical Society, Providence, RI, 1994. MR 1280712, DOI 10.1090/crmm/006

Neil Falkner and P. J. Fitzsimmons, Stopping distributions for right processes, Probab. Theory Related Fields 89 (1991), no. 3, 301–318. MR 1113221, DOI 10.1007/BF01198789

Masatoshi Fukushima, Y\B{o}ichi Ōshima, and Masayoshi Takeda, Dirichlet forms and symmetric Markov processes, De Gruyter Studies in Mathematics, vol. 19, Walter de Gruyter & Co., Berlin, 1994. MR 1303354, DOI 10.1515/9783110889741

R. K. Getoor, Excessive measures, Probability and its Applications, Birkhäuser Boston, Inc., Boston, MA, 1990. MR 1093669, DOI 10.1007/978-1-4612-3470-8

R. K. Getoor and M. J. Sharpe, Last exit times and additive functionals, Ann. Probability 1 (1973), 550–569. MR 353468, DOI 10.1214/aop/1176996885

Saunders MacLane and O. F. G. Schilling, Infinite number fields with Noether ideal theories, Amer. J. Math. 61 (1939), 771–782. MR 19, DOI 10.2307/2371335

Saunders MacLane and O. F. G. Schilling, Infinite number fields with Noether ideal theories, Amer. J. Math. 61 (1939), 771–782. MR 19, DOI 10.2307/2371335

G. A. Hunt, Markoff processes and potentials. III, Illinois J. Math. 2 (1958), 151–213. MR 107097

P. Erdös and T. Grünwald, On polynomials with only real roots, Ann. of Math. (2) 40 (1939), 537–548. MR 7, DOI 10.2307/1968938

Morgan Ward and R. P. Dilworth, The lattice theory of ova, Ann. of Math. (2) 40 (1939), 600–608. MR 11, DOI 10.2307/1968944

Frank Knight, Note on regularization of Markov processes, Illinois J. Math. 9 (1965), 548–552. MR 177450

18.

Paul Lévy, Théorie de l'Addition des Variables Aléatoires, Gauthier-Villars, Paris, 1937.

Michel Loève, Probability theory, 3rd ed., D. Van Nostrand Co., Inc., Princeton, N.J.-Toronto, Ont.-London, 1963. MR 0203748

Michel Loève, Paul Lévy, 1886–1971, Ann. Probability 1 (1973), no. 1, 1–18. MR 342337, DOI 10.1214/aop/1176997021

Zhi Ming Ma and Michael Röckner, Introduction to the theory of (nonsymmetric) Dirichlet forms, Universitext, Springer-Verlag, Berlin, 1992. MR 1214375, DOI 10.1007/978-3-642-77739-4

H. P. McKean Jr., A probabilitstic interpretation of equilibrium charge distributions, J. Math. Kyoto Univ. 4 (1964/65), 617–625. MR 185668, DOI 10.1215/kjm/1250524607

Daniel Ray, Resolvents, transition functions, and strongly Markovian processes, Ann. of Math. (2) 70 (1959), 43–72. MR 107302, DOI 10.2307/1969891

Tadashi Ueno, On recurrent Markov processes, K\B{o}dai Math. Sem. Rep. 12 (1960), 109–142. MR 119251

1.

Désiré André, Solution directe du problème résolu par M. Bertrand, C. R. Acad. Sci. Paris 105 (1887), 436-437.

2.

Kai Lai Chung, Probabilistic approach to the equilibrium problem, Ann. Inst. Fourier Grenoble 23 (1973), 313-322. MR 0391277

3.

-, Lectures from Markov Processes to Brownian Motion, Springer-Verlag, 1982. MR 0648601

4.

J. L. Doob, Semimartingales and subharmonic functions, Trans. Amer. Math. Soc. 77 (1954), 86-121. MR 16:269a

5.

-, Classical Potential Theory and its Probabilistic Counterpart, Springer-Verlag, 1984. MR 0731258

6.

D. A. Dawson, Measure-valued Markov processes, pp. 1-260 in Ecole d'Eté de Probabilités de Saint-Flour XXI - 1991 (editor: P. L. Hennequin), Lecture Notes in Mathematics, vol. 1541, Springer-Verlag, 1993. MR 1242575

7.

Eugene B. Dynkin, An Introduction to Branching Measure-Valued Processes, American Mathematical Society, 1994. MR 1280712

8.

Neil Falkner and P. J. Fitzsimmons, Stopping distributions for right processes, Probab. Th. Rel. Fields 89 (1991), 301-318. MR 1113221

9.

M. Fukushima, Y. Oshima, and M. Takeda, Dirichlet forms & symmetric Markov Processes, Walter de Gruyter, 1994. MR 1303354

10.

R. K. Getoor, Excessive Measures, Birkhäuser, 1990. MR 1093669

11.

R. K. Getoor and M. J. Sharpe, Last exit times and additive functionals, Ann. Probab. 1 (1973), 550-569. MR 0353468

12.

G. A. Hunt, Markov processes and potentials I, Illinois J. Math. 1 (1957), 44-93. MR 19:951g

13.

-, Markov processes and potentials II, Illinois J. Math. 1 (1957), 316-369. MR 19:951g

14.

-, Markov processes and potentials III, Illinois J. Math. 2 (1958), 151-213. MR 0107097

15.

Shizuo Kakutani, Two dimensional Brownian motion and harmonic functions, Proc. Imp. Acad. Tokyo 20 (1944), 707-714. MR 7:315b

16.

-, Markov processes and the Dirichlet problem, Proc. Japan Acad. 21 (1945), 227-233. MR 11:357h

17.

Frank Knight, Note on regularization of Markov processes, Illinois J. Math. 9 (1965), 548-552. MR 0177450

18.

Paul Lévy, Théorie de l'Addition des Variables Aléatoires, Gauthier-Villars, Paris, 1937.

19.

Michel Loève, Probability Theory, Third Edition, Van Nostrand, 1963. MR 0203748

20.

-, Paul Lévy, 1886-1971, Ann. Probab. 1 (1973), 1-18. MR 0342337

21.

Zhi-Ming Ma and Michael Rockner, Introduction to the theory of (non-symmetric) Dirichlet forms, Springer-Verlag, 1992. MR 1214375

22.

H. P. McKean, A probabilistic interpretation of equilibrium charge distributions, J. Math. Kyoto Univ. 4 (1965), 617-625. MR 0185668

23.

Daniel Ray, Resolvents, transition functions, and strongly Markovian processes, Ann. Math. 70 (1959), 43-72. MR 0107302

24.

T. Ueno, On recurrent Markov processes, Kôdai Math. Sem. Rep. 12 (1960), 109-142. MR 0119251