Geodesic
Non-anticipative Integral Transformations of Stochastic Processes
Publications de l'Institut Mathématique, _N_S_34 (1983) no. 48, p. 175

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Let $X$ be a stochastic process, defined on the interval $[0;1]$, and $Y$ its non-anticipative integral transformation defined by $ Y(t)=\int\limits^t_0 g(t, u) X(u)du $ In this paper we shall investigate conditions related to the family $ G=\{g(t,u), t\in[0;1],u \leq t\} $ under which the process $Y\!:\!1^\circ$ generates the spaces $H(Y;t)$ equal to the corresponding spaces $H(X;t)$ of the process $\bold X; 2\circ$ belongs to the same class as the process $X; 3^\circ$ is continuous, provided $X$ is continuous.
Classification : 60G05 60G12 
@article{PIM_1983_N_S_34_48_a26,
     author = {Ljiljana Petrovi\'c},
     title = {Non-anticipative {Integral} {Transformations} of {Stochastic} {Processes}},
     journal = {Publications de l'Institut Math\'ematique},
     pages = {175 },
     publisher = {mathdoc},
     volume = {_N_S_34},
     number = {48},
     year = {1983},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/PIM_1983_N_S_34_48_a26/}
}
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Ljiljana Petrović. Non-anticipative Integral Transformations of Stochastic Processes. Publications de l'Institut Mathématique, _N_S_34 (1983) no. 48, p. 175 . http://geodesic.mathdoc.fr/item/PIM_1983_N_S_34_48_a26/