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An introduction to nonstandard analysis and hyperfinite probability theory. (English) Zbl 0441.03027

Probabilistic analysis and related topics, Vol. 2, 105-142 (1979).

MSC:

03H05 Nonstandard models in mathematics
60H05 Stochastic integrals
60J25 Continuous-time Markov processes on general state spaces
28A25 Integration with respect to measures and other set functions
28A05 Classes of sets (Borel fields, \(\sigma\)-rings, etc.), measurable sets, Suslin sets, analytic sets
28A12 Contents, measures, outer measures, capacities
60J65 Brownian motion
60A05 Axioms; other general questions in probability
60A10 Probabilistic measure theory
03H10 Other applications of nonstandard models (economics, physics, etc.)
60G05 Foundations of stochastic processes
60A99 Foundations of probability theory
03-02 Research exposition (monographs, survey articles) pertaining to mathematical logic and foundations
60-02 Research exposition (monographs, survey articles) pertaining to probability theory
28-02 Research exposition (monographs, survey articles) pertaining to measure and integration