Bulletin of the American Mathematical Society

MathSciNet review: 1567942
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Book Information:

Author: Philip Protter
Title: Stochastic integration and differential equations—a new approach
Additional book information: Springer-Verlag, Berlin and New York, 1990, 302 pp., $48.00. ISBN-0-387-50996-8.

Klaus Bichteler, Stochastic integrators, Bull. Amer. Math. Soc. (N.S.) 1 (1979), no. 5, 761–765. MR 537627, DOI 10.1090/S0273-0979-1979-14655-X

Klaus Bichteler, Stochastic integration and $L^{p}$-theory of semimartingales, Ann. Probab. 9 (1981), no. 1, 49–89. MR 606798

K. L. Chung and R. J. Williams, Introduction to stochastic integration, 2nd ed., Probability and its Applications, Birkhäuser Boston, Inc., Boston, MA, 1990. MR 1102676, DOI 10.1007/978-1-4612-4480-6

C. Dellacherie, Un survol de la théorie de l’intégrale stochastique, Stochastic Process. Appl. 10 (1980), no. 2, 115–144 (French, with English summary). MR 587420, DOI 10.1016/0304-4149(80)90017-4

Claude Dellacherie and Paul-André Meyer, Probabilités et potentiel. Chapitres V à VIII, Revised edition, Actualités Scientifiques et Industrielles [Current Scientific and Industrial Topics], No. 1385, Hermann, Paris, 1980 (French). Théorie des martingales. [Martingale theory]. MR 566768

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

Richard Durrett, Brownian motion and martingales in analysis, Wadsworth Mathematics Series, Wadsworth International Group, Belmont, CA, 1984. MR 750829

J. Michael Harrison, Brownian motion and stochastic flow systems, Wiley Series in Probability and Mathematical Statistics: Probability and Mathematical Statistics, John Wiley & Sons, Inc., New York, 1985. MR 798279

11.

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

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

Jean Jacod, Calcul stochastique et problèmes de martingales, Lecture Notes in Mathematics, vol. 714, Springer, Berlin, 1979 (French). MR 542115

Ioannis Karatzas and Steven E. Shreve, Brownian motion and stochastic calculus, Graduate Texts in Mathematics, vol. 113, Springer-Verlag, New York, 1988. MR 917065, DOI 10.1007/978-1-4684-0302-2

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

H. P. McKean Jr., Stochastic integrals, Probability and Mathematical Statistics, No. 5, Academic Press, New York-London, 1969. MR 0247684

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 decomposition theorem for supermartingales, Illinois J. Math. 6 (1962), 193–205. MR 159359

P.-A. Meyer, Decomposition of supermartingales: the uniqueness theorem, Illinois J. Math. 7 (1963), 1–17. MR 144382

P.-A. Meyer, Intégrales stochastiques. I, II, III, IV, Séminaire de Probabilités (Univ. Strasbourg, Strasbourg, 1966/67) Springer, Berlin, 1967, pp. 72–94, 95–117, 118–141, 142–162 (French). MR 0231445

P. A. Meyer, Un cours sur les intégrales stochastiques, Séminaire de Probabilités, X (Seconde partie: Théorie des intégrales stochastiques, Univ. Strasbourg, Strasbourg, année universitaire 1974/1975), Lecture Notes in Math., Vol. 511, Springer, Berlin, 1976, pp. 245–400 (French). MR 0501332

P. A. Meyer, Notes sur les intégrales stochastiques. I. Intégrales hilbertiennes, Séminaire de Probabilités, XI (Univ. Strasbourg, Strasbourg, 1975/1976) Lecture Notes in Math., Vol. 581, Springer, Berlin, 1977, pp. 446–462 (French). MR 0501333

23.

L. C. G. Rogers, and D. Williams, Diffusions, Markov processes, and martingales, John Wiley and Sons, Chichester, 1987. MR 921238

L. C. G. Rogers and David Williams, Diffusions, Markov processes, and martingales. Vol. 2, Wiley Series in Probability and Mathematical Statistics: Probability and Mathematical Statistics, John Wiley & Sons, Inc., New York, 1987. Itô calculus. MR 921238

1.

K. Bichteler, Stochastic integrators, Bull. American Math. Soc. (N. S. ) 1 (1979), 761-765. MR 0537627

2.

K. Bichteler, Stochastic integration and L, Ann. Probab. 9 (1981), 49-89. MR 606798

3.

K. L. Chung, and R. J. Williams, Introduction to stochastic integration, Birkhäuser, Boston, 2nd edition, 1990. MR 1102676

4.

C. Dellacherie, Un survol de la théorie de l'intégrale stochastique, Stochastic Process. Appl. 10 (1980), 115-144. MR 587420

5.

C. Dellacherie, and P. A. Meyer, Probabilités and potentiel, vol. II, Hermann, Paris, 1980. MR 566768

6.

C. Doléans-Dade, and P. A. Meyer, Intégrales stochastiques par rapport aux martingales locales, Lecture Notes in Math., vol. 124, Springer-Verlag, New York, 1970, pp. 77-107. MR 270425

6A. C. Doléans-Dade, On the existence and unicity of solutions of stochastic differential equations, Z. Wahr. verw. Geb. 36 (1976), 93-101. MR 413270




7.

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

8.

R. Durrett, Brownian motion and martingales in analysis, Wadsworth, Belmont, CA, 1984. MR 750829

9.

J. M. Harrison, Brownian motion and stochastic flow systems, John Wiley and Sons, New York, 1985. MR 798279

10.

N. Ikeda and S. Watanabe, Stochastic differential equations, North-Holland, Amsterdam, 1981.

11.

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

12.

J. Jacod, Calcul stochastique et problèmes de martingales, Lecture Notes in Math., vol. 714, Springer-Verlag, New York, 1979. MR 542115

13.

I. Karatzas and S. E. Shreve, Brownian motion and stochastic calculus, Springer-Verlag, New York, 1988. MR 917065

14.

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

15.

H. P. McKean, Jr., Stochastic integrals, Academic Press, New York, 1969. MR 247684

16.

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

17.

P. A. Meyer, A decomposition theorem for supermartingales, Illinois J. Math. 6 (1962), 193-205. MR 159359

18.

P. A. Meyer, Decomposition of supermartingales: the uniqueness theorem, Illinois J. Math. 7(1963), 1-17. MR 144382

19.

P. A. Meyer, Intégrales stochastiques, I, II, III, IV, Séminaire de Probabilités I, Lecture Notes in Math., vol. 39, Springer-Verlag, New York, 1967, pp. 72-162. MR 231445

20.

P. A. Meyer, Un cours sur les intégrales stochastiques, Séminaire de Probabilités X, Lecture Notes in Math., vol. 511, Springer-Verlag, New York, 1976, pp. 246-400. MR 501332

21.

P. A. Meyer, Le théorème fondamental sur les martingales locales, Séminaire de Probabilités XI, Lecture Notes in Math., vol. 581, Springer-Verlag, New York, 1977, pp. 482-489. MR 501334

22.

D. Revuz, and M. Yor, Continuous martingales and Brownian motion (forthcoming book).

23.

L. C. G. Rogers, and D. Williams, Diffusions, Markov processes, and martingales, John Wiley and Sons, Chichester, 1987. MR 921238

23. L. C. G. Rogers, and D. Williams, Diffusions, Markov processes, and martingales, John Wiley and Sons, Chichester, 1987.