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Book Review

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Book Information:

Author: A. U. Kussmaul
Title: Stochastic integration and generalized martingales
Additional book information: Pitman Publishing, London, San Francisco, Melbourne, 1977, 163 pp., $14.00.

References [Enhancements On Off] (What's this?)

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  • 2. L. Bachelier, Théorie de la spéculation, Ann. Sci. École Norm. Sup. (3) 17 (1900), 21–86 (French). MR 1508978
  • 3. C. Dellacherie, Capacités et processus stochastiques, Springer-Verlag, Berlin and New York, 1972. MR 448504
  • 4. C. Doléans-Dade, Quelques applications de la formule de changement de variables pour les semimartingales, Z. Wahrscheinlichkeitstheorie und Verw. Gebiete 16 (1970), 181-194. MR 283883
  • 5. C. Doléans-Dade and P. A. Meyer, Intégrales stochastiques par rapport aux martingales locales, Lecture Notes in Math., vol. 124, Springer-Verlag, Berlin and New York, 1970, pp. 77-107. MR 270425
  • 6. J. L. Doob, Stochastic processes, Wiley, New York, 1953. MR 58896
  • 7. A. Einstein, On the movement of small particles suspended in a stationary liquid demanded by the molecular-kinetic theory of heat, Ann. Physik 17 (1905), 549-560; English Transl., Investigations on the theory of the Brownian movement, Methuen, London, 1926.
  • 8. L. I. Galčuk, The structure of a class of martingales, Proceedings of the School-Seminar on the Theory of Random Processes, (Druskininkai), Lithuanian SSR 1 (1974), 9-33. MR 410905
  • 9. K. Itô, Stochastic integral, Proc. Japan Acad. 20 (1944), 519-524. MR 14633
  • 10. H. Kunita, Stochastic integrals based on martingales taking values in Hilbert space, Nagoya Math. J. 38 (1970), 41-52. MR 264754
  • 11. H. Kunita and S. Watanabe, On square integrable martingales, Nagoya Math. J. 30 (1967), 209-245. MR 217856
  • 12. E. J. McShane, Stochastic calculus and stochastic models, Academic Press, New York, 1977. MR 443084
  • 13. E. J. McShane, Stochastic differential equations, J. Multivariate Anal. 5 (1975), 121-177. MR 373006
  • 14. M. Metivier, The stochastic integral with respect to processes with values in a reflexive Banach space, Theor. Probability 19 (1974), 758-787.
  • 15. M. Metivier and G. Pistone, Une formule d'isométrie pour l'intégrale stochastique Hilbertienne et équations d'évolution linéaires stochastiques, Z. Wahrscheinlichkeitstheorie und Verw. Gebiete 33 (1975), 1-18. MR 383527
  • 16. P. A. Meyer, A decomposition theorem for supermartingales, Illinois J. Math. 6 (1962), 193-205. MR 159359
  • 17. P. A. Meyer, Intégrales stochastiques. IV, Lecture Notes in Math., vol. 39, Springer-Verlag, Berlin and New York, 1967, pp. 142-162. MR 231445
  • 18. P. A. Meyer, Un cours sur les intégrales stochastiques, Lecture Notes in Math., vol. 511, Springer-Verlag, Berlin and New York, 1976, pp. 245-400. MR 501332
  • 19. P. A. Meyer, Intégrales Hilbertiennes, Lecture Notes in Math., vol. 581, Springer-Verlag, Berlin and New York, 1977, pp. 446-461. MR 501333
  • 20. R. E. A. C. Paley, N. Wiener, and A. Zygmund, Notes on random functions, Math. Z. 37 (1933), no. 1, 647–668. MR 1545426, https://doi.org/10.1007/BF01474606
  • 21. J. Pellaumail, Sur l'intégrale stochastique et la décomposition de Doob-Meyer, Asterique 9 (1973), 1-125. MR 339333
  • 22. Philip Protter, Markov solutions of stochastic differential equations, Z. Wahrsch. Verw. Gebiete 41 (1977/78), no. 1, 39–58. MR 477420, https://doi.org/10.1007/BF00535013
  • 23. P. E. Protter, A comparison of stochastic integrals, Ann. Probability (to appear).
  • 24. R. L. Stratonovich, A new representation for stochastic integrals and equations, SIAM. J. Control 4 (1966), 362-371. MR 196814
  • 25. N. Wiener, Differential-space, J. Math. and Physics 2 (1923), 131-174.

Review Information:

Reviewer: Philip Protter
Journal: Bull. Amer. Math. Soc. 84 (1978), 1346-1351
DOI: https://doi.org/10.1090/S0002-9904-1978-14572-8
American Mathematical Society