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

Book Review

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Book Information:

Authors: Sergio Albeverio, Raphael Høegh-Krohn, Jens Erik Fenstad and Tom Lindstrøm
Title: Nonstandard methods in stochastic analysis and mathematical physics
Additional book information: Academic Press, Orlando, xi + 514 pp., $59.50 cloth, $39.50 paperback. ISBN 0-12-048860-4.

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

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  • 2. Martin Davis, Applied nonstandard analysis, Wiley, New York, 1977. MR 505473
  • 3. C. Ward Henson and H. Jerome Keisler, On the strength of nonstandard analysis, J. Symbolic Logic 51 (1986), no. 2, 377–386. MR 840415, https://doi.org/10.2307/2274061
  • 4. Albert Hurd and Peter Loeb (eds. ), Victoria Symposium on Nonstandard Analysis, Lecture Notes in Math., vol. 369, Springer-Verlag, Berlin and New York, 1974. MR 472459
  • 5. Albert Emerson Hurd (ed.), Nonstandard analysis—recent developments, Lecture Notes in Mathematics, vol. 983, Springer-Verlag, Berlin-New York, 1983. Including papers presented at the Second Victoria Symposium on Nonstandard Analysis held at the University of Victoria, Victoria, B.C., 1980. MR 698951
  • 6. 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
  • 7. 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
  • 8. P. A. Loeb, Conversion from nonstandard to standard measure spaces and applications in probability theory, Trans. Amer. Math. Soc. 211 (1975), 113-122. MR 390154
  • 9. Robert Lutz and Michel Goze, Nonstandard analysis, Lecture Notes in Mathematics, vol. 881, Springer-Verlag, Berlin-New York, 1981. A practical guide with applications; With a foreword by Georges H. Reeb. MR 643624
  • 10. W. A. J. Luxemburg (ed. ), Applications of model theory to algebra, analysis, and probability, Holt, Rinehart and Winston, New York, 1969. MR 234829
  • 11. W. A. J. Luxemburg and A. Robinson (eds. ), Contributions to non-standard analysis, North-Holland, Amsterdam, 1972. MR 476972
  • 12. Edwin Perkins, A global intrinsic characterization of Brownian local time, Ann. Probab. 9 (1981), no. 5, 800–817. MR 628874
  • 13. Alain Robert, Analyse non standard, Presses Polytechniques Romandes, Lausanne, 1985 (French). MR 801723
  • 14. A. Robinson, Introduction to model theory and to the metamathematics of algebra, North-Holland, Amsterdam, 1963. MR 153570
  • 15. A. Robinson, Non-standard analysis, North-Holland, Amsterdam, 1966. MR 205854
  • 16. A. Robinson and A. H. Lightstone, Nonarchimedean fields and asymptotic expansions, North-Holland, Amsterdam, 1975. MR 414354
  • 17. K. Stroyan and W. A. J. Luxemburg, Introduction to the theory of infinitesimals, Academic Press, New York, 1976. MR 491163
  • 18. K. D. Stroyan and José Manuel Bayod, Foundations of infinitesimal stochastic analysis, Studies in Logic and the Foundations of Mathematics, vol. 119, North-Holland Publishing Co., Amsterdam, 1986. MR 849100

Review Information:

Reviewer: A. E. Hurd
Journal: Bull. Amer. Math. Soc. 17 (1987), 385-389
DOI: https://doi.org/10.1090/S0273-0979-1987-15607-2
American Mathematical Society