Bulletin of the American Mathematical Society

MathSciNet review: 1567651
Full text of review: PDF   This review is available free of charge.
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.

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

Martin Davis, Applied nonstandard analysis, Pure and Applied Mathematics, Wiley-Interscience [John Wiley & Sons], New York-London-Sydney, 1977. MR 0505473

C. Ward Henson and H. Jerome Keisler, On the strength of nonstandard analysis, J. Symbolic Logic 51 (1986), no. 2, 377–386. MR 840415, DOI 10.2307/2274061

Albert Hurd and Peter Loeb (eds.), Victoria Symposium on Nonstandard Analysis, Lecture Notes in Mathematics, Vol. 369, Springer-Verlag, Berlin-New York, 1974. Held at the University of Victoria, Victoria, B. C., 8–11 May 1972. MR 0472459

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

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

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

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

W. A. J. Luxemburg (ed.), Applications of model theory to algebra, analysis, and probability. , Holt, Rinehart and Winston, New York-Montreal, Que.-London, 1969. MR 0234829

Contributions to non-standard analysis, Studies in Logic and the Foundations of Mathematics, Vol. 69, North-Holland Publishing Co., Amsterdam-London, 1972. A collection of papers based on lectures given at the Symposium on Non-standard Analysis, Oberwolfach, July 19–July 25, 1970; Edited by W. A. J. Luxemburg and A. Robinson. MR 0476972

Edwin Perkins, A global intrinsic characterization of Brownian local time, Ann. Probab. 9 (1981), no. 5, 800–817. MR 628874

Alain Robert, Analyse non standard, Presses Polytechniques Romandes, Lausanne, 1985 (French). MR 801723

Abraham Robinson, Introduction to model theory and to the metamathematics of algebra, North-Holland Publishing Co., Amsterdam, 1963. MR 0153570

Abraham Robinson, Non-standard analysis, North-Holland Publishing Co., Amsterdam, 1966. MR 0205854

A. H. Lightstone and Abraham Robinson, Nonarchimedean fields and asymptotic expansions, North-Holland Mathematical Library, Vol. 13, North-Holland Publishing Co., Amsterdam-Oxford; American Elsevier Publishing Co., Inc., New York, 1975. MR 0414354

K. D. Stroyan and W. A. J. Luxemburg, Introduction to the theory of infinitesimals, Pure and Applied Mathematics, No. 72, Academic Press [Harcourt Brace Jovanovich, Publishers], New York-London, 1976. MR 0491163

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

1.

R. Anderson, A non-standard representation for Brownian motion and Itô integration, Israel J. Math. 25 (1976), 15-46. MR 0464380

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), 377-386. MR 840415

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.

A. E. Hurd (ed. ), Nonstandard analysis--recent developments, Lecture Notes in Math., vol. 983, Springer-Verlag, Berlin and New York, 1983. MR 698951

6.

A. E. Hurd and P. A. Loeb, An introduction to nonstandard real analysis, Academic Press, Orlando, 1985. MR 806135

7.

H. Jerome Keisler, An infinitesimal approach to stochastic analysis, Mem. Amer. Math. Soc. No. 297 (1984). MR 732752

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.

R. Lutz and M. Goze, Nonstandard analysis, Lecture Notes in Math., vol. 881, Springer-Verlag, Berlin, 1981. 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.

E. Perkins, A global intrinsic characterization of local time, Ann. Probability 9 (1981), 800-817. MR 628874

13.

Alain Robert, Analyse non standard, Presses Polytechniques Romandes, Lausanne, 1985. 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. Stroyan and J. M. Bayod, Foundations of infinitesimal stochastic analysis, North-Holland, Amsterdam, 1986. MR 849100