Book Review
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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, NorthHolland, Amsterdam, 1986, xii + 478 pp., $47.50. ISBN 0444879277.
 Sergio Albeverio, Raphael HøeghKrohn, 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

[A1] R. M. Anderson, A nonstandard representation for Brownian motion and ltô integration, Israel J. Math. 25 (1976), 1546. MR 464380

[A2] R. M. Anderson, Review of [HL], Bull. Amer. Math. Soc. (N. S. ) 16 (1987), 298306.
 Nigel J. Cutland, Nonstandard measure theory and its applications, Bull. London Math. Soc. 15 (1983), no. 6, 529–589. MR 720746, https://doi.org/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, https://doi.org/10.1007/BFb0065334
 H. Jerome Keisler, An infinitesimal approach to stochastic analysis, Mem. Amer. Math. Soc. 48 (1984), no. 297, x+184. MR 732752, https://doi.org/10.1090/memo/0297

[L] P. A. Loeb, Conversion from standard to standard measure spaces and applications to probability theory, Trans. Amer. Math. Soc. 211 (1975), 113122. MR 390154
 Edward Nelson, Radically elementary probability theory, Annals of Mathematics Studies, vol. 117, Princeton University Press, Princeton, NJ, 1987. MR 906454
Review Information:
Reviewer: D. N. Hoover
Journal: Bull. Amer. Math. Soc. 21 (1989), 287292
DOI: https://doi.org/10.1090/S027309791989158321