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Non-anticipative integral transformations of stochastic processes. (English) Zbl 0548.60038

Summary: Let X be a stochastic process defined on the interval [0;1], and Y its non-anticipative integral transformation defined by (1) \(Y(t)=\int^{t}_{0}g(t,u)X(u)du\). In this paper we shall investigate conditions related to the family (2) \(G=\{g(t,u)\), \(t\in [0;1]\), \(u\leq t\}\) under which the process Y(1) generates the spaces H(Y;t) equal to the corresponding spaces H(X;t) of the process X;(2) belongs to the same class as the process X;(3) is continuous, provided X is continuous.

MSC:

60G05 Foundations of stochastic processes
60G12 General second-order stochastic processes
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