Bulletin of the American Mathematical Society

MathSciNet review: 1567758
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Book Information:

Author: Edward Nelson
Title: Radically elementary probability theory
Additional book information: Annals of Mathematical Studies, vol. 117, Princeton University Press, Princeton, N. J., 1987, ix + 97 pp., $40.00 ($15.00 paperback). ISBN 0-691-08473-4.

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

3.

M. Davis, Review of "Internal set theory" by E. Nelson, J. Symbolic Logic 48 (1983), 1203-12004.

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

Edward Nelson, Internal set theory: a new approach to nonstandard analysis, Bull. Amer. Math. Soc. 83 (1977), no. 6, 1165–1198. MR 469763, DOI 10.1090/S0002-9904-1977-14398-X

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

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

1.

S. Albeverio, J. E. Fenstad, R. Heogh-Krohn, and T. Lindstrom, Nonstandard methods in stochastic analysis and mathematical physics, Academic Press, Orlando, 1986. MR 0859372

2.

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

3.

M. Davis, Review of "Internal set theory" by E. Nelson, J. Symbolic Logic 48 (1983), 1203-12004.

4.

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

5.

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

6.

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

7.

E. Nelson, Internal set theory: A new approach to nonstandard analysis, Bull. Amer. Math. Soc. 83 (1977), 1165-1198. MR 469763

8.

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

9.

A. Robinson, Non-standard analysis, (2nd ed.), North-Holland, Amsterdam, 1974 (1st ed., 1966). MR 205854