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Book Review
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Book Information
Author(s):
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
References:
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- 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
Additional Information:
Reviewer(s):
R. J.
Williams
Review Information:
Journal:
Bull. Amer. Math. Soc.
25
(1991),
170-180.
DOI:
10.1090/S0273-0979-1991-16058-1
PII:
S 0273-0979(1991)16058-1
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