Bulletin of the American Mathematical Society

MathSciNet review: 1567801
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Book Information:

Authors: K. D. Stroyan and J. M. Bayod
Title: Foundations of infinitesimal stochastic analysis
Additional book information: Studies in Logic and the Foundations of Mathematics, vol. 119, North-Holland, Amsterdam, 1986, xii + 478 pp., $47.50. ISBN 0-444-87927-7.

Sergio Albeverio, Raphael Høegh-Krohn, Jens Erik Fenstad, and Tom Lindstrøm, Nonstandard methods in stochastic analysis and mathematical physics, Pure and Applied Mathematics, vol. 122, Academic Press, Inc., Orlando, FL, 1986. MR 859372

Robert M. Anderson, A non-standard representation for Brownian motion and Itô integration, Israel J. Math. 25 (1976), no. 1-2, 15–46. MR 464380, DOI 10.1007/BF02756559

[A2] R. M. Anderson, Review of [HL], Bull. Amer. Math. Soc. (N. S. ) 16 (1987), 298-306.

Nigel J. Cutland, Nonstandard measure theory and its applications, Bull. London Math. Soc. 15 (1983), no. 6, 529–589. MR 720746, DOI 10.1112/blms/15.6.529

Albert E. Hurd and Peter A. Loeb, An introduction to nonstandard real analysis, Pure and Applied Mathematics, vol. 118, Academic Press, Inc., Orlando, FL, 1985. MR 806135

C. Ward Henson and L. C. Moore Jr., Nonstandard analysis and the theory of Banach spaces, Nonstandard analysis—recent developments (Victoria, B.C., 1980) Lecture Notes in Math., vol. 983, Springer, Berlin, 1983, pp. 27–112. MR 698954, DOI 10.1007/BFb0065334

H. Jerome Keisler, An infinitesimal approach to stochastic analysis, Mem. Amer. Math. Soc. 48 (1984), no. 297, x+184. MR 732752, DOI 10.1090/memo/0297

Peter A. Loeb, Conversion from nonstandard to standard measure spaces and applications in probability theory, Trans. Amer. Math. Soc. 211 (1975), 113–122. MR 390154, DOI 10.1090/S0002-9947-1975-0390154-8

Edward Nelson, Radically elementary probability theory, Annals of Mathematics Studies, vol. 117, Princeton University Press, Princeton, NJ, 1987. MR 906454, DOI 10.1515/9781400882144

[AFH-KE] Albeverio, J. E. Fenstad, R. Høegh-Krohn, and T. Lindstrøm, Nonstandard methods in stochastic analysis and mathematical physics, Academic Press, New York, 1986. MR 0859372




[A1] R. M. Anderson, A nonstandard representation for Brownian motion and ltô integration, Israel J. Math. 25 (1976), 15-46. MR 464380




[A2] R. M. Anderson, Review of [HL], Bull. Amer. Math. Soc. (N. S. ) 16 (1987), 298-306.




[C] N. J. Cutland, Nonstandard measure theory and its applications, J. London Math. Soc. 15 (1983), 529-589. MR 720746




[HL] A. E. Hurd and P. A. Loeb, An Introduction to nonstandard real analysis, Academic Press, New York, 1985. MR 806135




[HM] C. W. Henson and L. C. Moore, Nonstandard analysis and the theory of Banach spaces, (A. E. Hurd, ed. ), Nonstandard Analysis: Recent Developments, Lecture Notes in Math., vol. 983, Springer-Verlag, Berlin and New York, 1983. MR 698954




[K] H. J. Keisler, An infinitesimal approach to stochastic analysis, Mem. Amer. Math. Soc. 48, (1984), no. 297.. MR 732752




[L] P. A. Loeb, Conversion from standard to standard measure spaces and applications to probability theory, Trans. Amer. Math. Soc. 211 (1975), 113-122. MR 390154




[N] E. Nelson, Radically elementary probability theory, Ann. of Math. Studies no. 117, Princeton Univ. Press, Princeton, N. J., 1987. MR 906454