On Realizability of Stochastic Processes

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


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.


Sample Path Unit Interval Modulus Function Nondecreasing Function Fixed Class 
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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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