On Realizability of Stochastic Processes
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.
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