Papers and books using NSA in probability.


AMS - American Mathematical Society

APAL -Annals of Pure and Applied Logic

NSA - Nonstandard analysis

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Anderson R (1976) A non-standard representation for Brownian motion and Ito integration. Israel Journal of Mathematics 25 pp 15-46

Gauthier Y (1993) La logique interne de la theorie des probabilites. Dialogue (Canadian) Vol 32 #1 pp 95-104.

Helms L and Loeb P (1982) A nonstandard proof of the martingale convergence theorem. Rocky Mountain J. Math. 12

Hoover D and Perkins E (1983) Nonstandard constructions of the stochastic integral and applications to stochastic differential equations I, II. Trans. AMS 275 pp 1-58

Keisler H.J. (1984) An infinitesimal approach to stochastic analysis. Memoirs AMS 297

Keisler H.J. (1986) Hyperfinite models for adapted prob. logic APAL 31 pp 71-86

Keisler H.J. (1988) Infinitesimals in probability theory; in NSA and its applications, Cutland N ed, Cambridge U. Press.

Keisler H.J. (1991) From discrete to continuous time. APAL 52 pp 99-141

Lawler G (1986) Gaussian behavior of loop-erased, self-avoiding random walk in four dimensions. Duke Math. J. 53 pp 249-270

Lindstrøm T (1983) Stochastic integration in hyperfinite dimensional linear spaces. In (Hurd A ed) NSA - recent developments. Springer-Verlag, NY, Berlin.

Loeb P (1975) Conversion from nonstandard to standard measure spaces with applications in probability theory. Transactions of the AMS 211 pp 113-122

Loeb P (1979) An introduction to NSA and hyperfinite probability theory; in Probabilistic Analysis and related topics pp 105-142 (Bharucha-Reid A ed.) Academic Press New York

Miller D (1969) Nonstandard proofs of invariance principles in probability theory. In (Luxemburg W ed) Applications of Model Theory to Algebra, Analysis and Probabilty. Holt, Rinehart and Winston, NY

Nelson E (1987) Radically elementary probability theory. Annals of Math. Studies 117 Princeton Univ. Press, Princeton NJ.

Ozeki K (1980) A new definition of the entropy of general probability-distributions based on the NSA. Information and Control 47 #2 pp 94-106

Perkins E (1983) Stochastic processes and NSA; in NSA - recent developments, Hurd A ed, Lecture Notes in Math. 983 Springer-Verlag

Rodenhausen H (1982) A characterisation of nonstandard liftings of measurable functions and stochastic processes. Israel J. Math. 43

Stoll A (1986) A nonstandard construction of Levy Brownian motion. Prob. thy. and related fields 71 pp 321-334

Stroyan K and Bayod J (1986) Foundations of infinitesimal stochastic analysis. North-Holland, Amsterdam.

Sun Y (1996) Hyperfinite law of large numbers. Bulletin of Symbolic Logic Vol 2 #2 pp 189-198