Petrović, Ljiljana Non-anticipative integral transformations of stochastic processes. (English) Zbl 0548.60038 Publ. Inst. Math., Nouv. Sér. 34(48), 175-182 (1983). 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 Keywords:non-anticipative integral transformation PDFBibTeX XMLCite \textit{L. Petrović}, Publ. Inst. Math., Nouv. Sér. 34(48), 175--182 (1983; Zbl 0548.60038) Full Text: EuDML