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On Realizability of Stochastic Processes

  • Peter Gaenssler
  • Winfried Stute
Part of the Czechoslovak Academy of Sciences book series (TPCI, volume 8A)

Abstract

Let ξ = (ξt)0≤t≤1 be a stochastic process on some probability space (Ω, ℱ ℙ) and let X be a fixed class of real functions on the unit interval. Then, by definition, ξ is said to have a realization in X, if there exists a process n = (ηt)0≤t≤1 with sample paths in X and such that ξ and η have the same finite dimensional distributions. It is the purpose of this paper to point out the strong interdependence between realizability in X and the behaviour of a corresponding modulus function.

Keywords

Sample Path Unit Interval Modulus Function Nondecreasing Function Fixed Class 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© ACADEMIA, Publishing House of the Czechoslovak Academy of Sciences, Prague 1978

Authors and Affiliations

  • Peter Gaenssler
    • 1
  • Winfried Stute
    • 1
  1. 1.Mathematisches InstitutRuhr-Universität BochumBochumBundesrepublik Deutschland

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