Remote Access Bulletin of the American Mathematical Society

Bulletin of the American Mathematical Society

ISSN 1088-9485(online) ISSN 0273-0979(print)

Book Review

The AMS does not provide abstracts of book reviews. You may download the entire review from the links below.


Full text of review: PDF
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?)

  • 1. Ludwig Arnold, Stochastic differential equations: theory and applications, Wiley-Interscience [John Wiley & Sons], New York-London-Sydney, 1974. Translated from the German. MR 0443083
  • 2. L. Bachelier, Théorie de la spéculation, Ann. Sci. École Norm. Sup. (3) 17 (1900), 21–86 (French). MR 1508978
  • 3. Claude Dellacherie, Capacités et processus stochastiques, Springer-Verlag, Berlin-New York, 1972 (French). Ergebnisse der Mathematik und ihrer Grenzgebiete, Band 67. MR 0448504
  • 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 (French). MR 0283883
  • 5. 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
  • 6. J. L. Doob, Stochastic processes, John Wiley & Sons, Inc., New York; Chapman & Hall, Limited, London, 1953. MR 0058896
  • 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. Gal′čuk, The structure of certain martingales, Proceedings of the School and Seminar on the Theory of Random Processes (Druskininkai, 1974) Inst. Fiz. i Mat. Akad. Nauk Litovsk. SSR, Vilnius, 1975, pp. 9–33 (Russian). MR 0410905
  • 9. Kiyosi Itô, Stochastic integral, Proc. Imp. Acad. Tokyo 20 (1944), 519–524. MR 0014633
  • 10. Hiroshi Kunita, Stochastic integrals based on martingales taking values in Hilbert space, Nagoya Math. J. 38 (1970), 41–52. MR 0264754
  • 11. Hiroshi Kunita and Shinzo Watanabe, On square integrable martingales, Nagoya Math. J. 30 (1967), 209–245. MR 0217856
  • 12. E. J. McShane, Stochastic calculus and stochastic models, Academic Press, New York-London, 1974. Probability and Mathematical Statistics, Vol. 25. MR 0443084
  • 13. E. J. McShane, Stochastic differential equations, J. Multivariate Anal. 5 (1975), 121–177. MR 0373006
  • 14. M. Metivier, The stochastic integral with respect to processes with values in a reflexive Banach space, Theor. Probability 19 (1974), 758-787.
  • 15. Michel Métivier and Giovanni Pistone, Une formule d’isométrie pour l’intégrale stochastique hilbertienne et équations d’évolution linéaires stochastiques, Z. Wahrscheinlichkeitstheorie und Verw. Gebiete 33 (1975/76), no. 1, 1–18 (French). MR 0383527
  • 16. P. A. Meyer, A decomposition theorem for supermartingales, Illinois J. Math. 6 (1962), 193–205. MR 0159359
  • 17. 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
  • 18. 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), Springer, Berlin, 1976, pp. 245–400. Lecture Notes in Math., Vol. 511 (French). MR 0501332
  • 19. P. A. Meyer, Notes sur les intégrales stochastiques. I. Intégrales hilbertiennes, Séminaire de Probabilités, XI (Univ. Strasbourg, Strasbourg, 1975/1976), Springer, Berlin, 1977, pp. 446–462. Lecture Notes in Math., Vol. 581 (French). MR 0501333
  • 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, 10.1007/BF01474606
  • 21. Jean Pellaumail, Sur l’intégrale stochastique et la décomposition de Doob-Meyer, Société Mathématique de France, Paris, 1973 (French). Astérisque, No. 9. MR 0339333
  • 22. Philip Protter, Markov solutions of stochastic differential equations, Z. Wahrsch. Verw. Gebiete 41 (1977/78), no. 1, 39–58. MR 477420, 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 0196814
  • 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