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A generalization of Kolmogorov’s extension theorem and an application to the construction of stochastic processes with random time domains. (English) Zbl 0643.60032

According to Kolmogorov’s familiar extension theorem, a consistent system of finite-dimensional distributions determines uniquely a probability measure on the appropriate product space \(\Pi \{S_ t:t\in T\}\). The latter is a space of functions with domain T, and the present paper establishes an extension of Kolmogorov’s theorem to spaces of functions with possibly different domains (“random domains”).
The result obtained implies earlier results of S. E. Kuznetsov [Theory Probab. Appl. 18, 571-575 (1973; Zbl 0296.60049)] and E. B. Dynkin [Stochastic analysis, Proc. int. Conf., Evanston/Ill. 1978; 63-77 (1978; Zbl 0494.60074)] on the existence of stochastic processes on random time intervals.
Reviewer: F.Papangelou

MSC:

60G05 Foundations of stochastic processes
28C20 Set functions and measures and integrals in infinite-dimensional spaces (Wiener measure, Gaussian measure, etc.)
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