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

MSC:
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
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[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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