Bulletin of the American Mathematical Society

MathSciNet review: 1567506
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Book Information:

Author: Michel Métivier
Title: Semimartingales, a course on stochastic processes
Additional book information: dc Gruyter Studies in Mathematics, Vol. 2, Walter de Gruyter & Co., Berlin, 1982, xi + 287 pp., DM 88.--, $40.00. ISBN 3-1100--8674-3.

Temps locaux, Astérisque, vol. 52, Société Mathématique de France, Paris, 1978 (French). Exposés du Séminaire J. Azéma-M. Yor; Held at the Université Pierre et Marie Curie, Paris, 1976–1977; With an English summary. MR 509476

Jacques Azéma and Marc Yor (eds.), Séminaire de Probabilités. XVI, Lecture Notes in Mathematics, vol. 920, Springer-Verlag, Berlin-New York, 1982 (French). Held in 1980–1981. MR 658668

Alain Bensoussan, Stochastic control by functional analysis methods, Studies in Mathematics and its Applications, vol. 11, North-Holland Publishing Co., Amsterdam-New York, 1982. MR 652685

Kai Lai Chung and R. J. Williams, Introduction to stochastic integration, Progress in Probability and Statistics, vol. 4, Birkhäuser Boston, Inc., Boston, MA, 1983. MR 711774, DOI 10.1007/978-1-4757-9174-7

Claude Dellacherie and Paul-André Meyer, Probabilities and potential, North-Holland Mathematics Studies, vol. 29, North-Holland Publishing Co., Amsterdam-New York, 1978. MR 521810

Claude Dellacherie and Paul-André Meyer, Probabilities and potential. B, North-Holland Mathematics Studies, vol. 72, North-Holland Publishing Co., Amsterdam, 1982. Theory of martingales; Translated from the French by J. P. Wilson. MR 745449

C. Doléans-Dade and P.-A. Meyer, Intégrales stochastiques par rapport aux martingales locales, Séminaire de Probabilités, IV (Univ. Strasbourg, 1968/69) Lecture Notes in Mathematics, Vol. 124, Springer, Berlin, 1970, pp. 77–107 (French). MR 0270425

Catherine Doléans-Dade, On the existence and unicity of solutions of stochastic integral equations, Z. Wahrscheinlichkeitstheorie und Verw. Gebiete 36 (1976), no. 2, 93–101. MR 413270, DOI 10.1007/BF00533992

J. L. Doob, Stochastic processes, John Wiley & Sons, Inc., New York; Chapman & Hall, Ltd., London, 1953. MR 0058896

Robert J. Elliott, Stochastic calculus and applications, Applications of Mathematics (New York), vol. 18, Springer-Verlag, New York, 1982. MR 678919

Wendell H. Fleming and Raymond W. Rishel, Deterministic and stochastic optimal control, Applications of Mathematics, No. 1, Springer-Verlag, Berlin-New York, 1975. MR 0454768

12.

W. H. Fleming, Book review, Bull. Amer. Math. Soc. (N.S.) 7 (1982), 411-414.

Nobuyuki Ikeda and Shinzo Watanabe, Stochastic differential equations and diffusion processes, 2nd ed., North-Holland Mathematical Library, vol. 24, North-Holland Publishing Co., Amsterdam; Kodansha, Ltd., Tokyo, 1989. MR 1011252

Kiyosi Itô, Stochastic integral, Proc. Imp. Acad. Tokyo 20 (1944), 519–524. MR 14633

Kiyosi Ito, On stochastic differential equations, Mem. Amer. Math. Soc. 4 (1951), 51. MR 40618

J. Jacod, J. Mémin, and M. Métivier, On tightness and stopping times, Stochastic Process. Appl. 14 (1983), no. 2, 109–146. MR 679668, DOI 10.1016/0304-4149(83)90067-4

Hiroshi Kunita and Shinzo Watanabe, On square integrable martingales, Nagoya Math. J. 30 (1967), 209–245. MR 217856

J.-F. Le Gall, Applications du temps local aux équations différentielles stochastiques unidimensionnelles, Seminar on probability, XVII, Lecture Notes in Math., vol. 986, Springer, Berlin, 1983, pp. 15–31 (French). MR 770393, DOI 10.1007/BFb0068296

Hayri Körezlioğlu and Jacques Szpirglas (eds.), Processus aléatoires à deux indices, Lecture Notes in Mathematics, vol. 863, Springer, Berlin, 1981 (French). Papers from the E.N.S.T.-C.N.E.T. Colloquium held in Paris, June 30–July 1, 1980. MR 630302

20.

R. Sh. Lipster and A. N. Shiryayev, Statistics of random processes, vols. 1, 2, Springer-Verlag, New York, 1977.

Michel Métivier and Jean Pellaumail, Stochastic integration, Probability and Mathematical Statistics, Academic Press [Harcourt Brace Jovanovich, Publishers], New York-London-Toronto, Ont., 1980. MR 578177

P.-A. Meyer, A differential geometric formalism for the Itô calculus, Stochastic integrals (Proc. Sympos., Univ. Durham, Durham, 1980) Lecture Notes in Math., vol. 851, Springer, Berlin-New York, 1981, pp. 256–270. MR 620993

Philip Protter, Markov solutions of stochastic differential equations, Z. Wahrsch. Verw. Gebiete 41 (1977/78), no. 1, 39–58. MR 477420, DOI 10.1007/BF00535013

24.

P. E. Protter, Book Review, Bull. Amer. Math. Soc. 6 (1978), 1346-1351.

Daniel W. Stroock and S. R. Srinivasa Varadhan, Multidimensional diffusion processes, Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], vol. 233, Springer-Verlag, Berlin-New York, 1979. MR 532498

26.

E. Wong, Stochastic processes in information and dynamical systems, McGraw-Hill, 1971 (2nd ed., Springer Verlag (to appear)).

1.

J. Azema and M. Yor (Editors), Temps locaux, Asterisque 52-53, 1978. MR 0509476

2.

J. Azema and M. Yor (Editors), Supplement Différentielle Stochastique, Séminaire de Probabilités. XVI, Lecture Notes in Math., vol. 921, Springer-Verlag, New York, 1982. MR 658668

3.

A. Bensoussan, Stochastic control by functional analysis methods, North-Holland, 1982. MR 652685

4.

K. L. Chung and R. J. Williams, Introduction to stochastic integration, Birkhäuser, Boston, 1983. MR 711774

5.

C. Dellacherie and P. A. Meyer, Probabilities and potential, North-Holland, 1978. (French original 1975). MR 521810

6.

C. Dellacherie and P. A. Meyer, Probabilities and potential B, theory of martingales, North-Holland, 1982. (French original 1980). MR 745449

7.

C. Doléans-Dade and P. A. Meyer, Intégrales stochastique par rapport aux martingales locales, Séminaire de Probabilités IV, Lecture Notes in Math., vol. 124, Springer-Verlag, 1970, pp. 77-107. MR 270425

8.

C. Doléans-Dade, On the existence and unicity of solutions of stochastic integral equations, Z. Wahrsch. Verw. Gebiete 29 (1976), 109-122. MR 413270

9.

J. L. Doob, Stochastic processes, Wiley, New York, 1953. MR 58896

10.

R. J. Elliott, Stochastic calculus and applications, Springer-Verlag, New York, 1982. MR 678919

11.

W. H. Fleming and R. W. Rishel, Deterministic and stochastic optimal control, Springer-Verlag, New York, 1975. MR 454768

12.

W. H. Fleming, Book review, Bull. Amer. Math. Soc. (N.S.) 7 (1982), 411-414.

13.

N. Ikeda and S. Watanabe, Stochastic differential equations and diffusion processes, North Holland, 1981. MR 1011252

14.

K. Itô, Stochastic integral, Proc. Japan Acad. 20 (1944), 519-524. MR 14633

15.

K. Itô, On stochastic differential equations, Mem. Amer. Math. Soc. 4 (1951), 1-51. MR 40618

16.

J. Jacob, J. Memin and M. Métivier, On tightness and stopping times, Stochastic Process Appl. 14 (1983), 109-146. MR 679668

17.

H. Kunita and S. Watanabe, On square integrable martingales, Nagoya Math. J. 30 (1967), 209-245. MR 217856

18.

J. F. Le Gall, Application du temps local aux équation différentielles stochastique unidimensionelles, Séminaire de Probabilités XVII, Lecture Notes in Math., vol. 986, Springer-Verlag, 1982, pp. 15-31. MR 770393

19.

H. Korezlioglu, G. Mazziotto and J. Szpirglas (Editors), Processus aléatoires à deux indices, Lecture Notes in Math., vol. 863, Springer-Verlag, New York, 1981. MR 630302

20.

R. Sh. Lipster and A. N. Shiryayev, Statistics of random processes, vols. 1, 2, Springer-Verlag, New York, 1977.

21.

M. Métivier and J. Pellaumail, Stochastic integration, Academic Press, New York, 1980. MR 578177

22.

P. A. Meyer, A differential geometric formalism for the Itô calculus, Stochastic Integrals, Lecture Notes in Math., vol. 851, Springer-Verlag, New York, 1981, pp. 256-270. MR 620993

23.

P. E. Protter, Markov solutions of stochastic differential equations, Z. Wahrsch. Verw. Gebiete 41 (1977), 39-58. MR 477420

24.

P. E. Protter, Book Review, Bull. Amer. Math. Soc. 6 (1978), 1346-1351.

25.

D. W. Stroock and S. R. S. Varadhan, Multidimensional diffusion processes, Springer-Verlag, New York, 1979. MR 532498

26.

E. Wong, Stochastic processes in information and dynamical systems, McGraw-Hill, 1971 (2nd ed., Springer Verlag (to appear)).