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A characterization of nonstandard liftings of measurable functions and stochastic processes. (English) Zbl 0504.60003

60A10 Probabilistic measure theory
03H05 Nonstandard models in mathematics
60G17 Sample path properties
28A20 Measurable and nonmeasurable functions, sequences of measurable functions, modes of convergence
60G05 Foundations of stochastic processes
Full Text: DOI
[1] R. Anderson,A non-standard representation for Brownian motion and Itô integration, Isr. J. Math.25 (1976), 15–46. · Zbl 0353.60052 · doi:10.1007/BF02756559
[2] P.R. Halmos,Measure Theory, D. van Nostrand Co., Inc., Princeton, New Jersey, 1950.
[3] H. J. Keisler,Hyperfinite Model Theory, inLogic Colloquium 76 (R. O. Gandy and J. M. E. Hyland, eds.), North-Holland, 1977, pp. 5–110.
[4] H. J. Keisler,An infinitesimal approach to stochastic analysis, Am. Math. Soc. Memoris, to appear. · Zbl 0529.60062
[5] T. Lindström,Hyperfinite stochastic integration I, II, III, Math. Scand.46 (1980). · Zbl 0444.60043
[6] P. Loeb,Conversion from non-standard to standard measure spaces and applications to probability theory, Trans. Am. Math. Soc.211 (1975), 113–122. · Zbl 0312.28004 · doi:10.1090/S0002-9947-1975-0390154-8
[7] K. D. Stroyan and W. A. J. Luxemburg,Introduction to the Theory of Infinitesimals, Academic Press, 1976.
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