Canonical representations of second order stochastic processes
Teoriâ veroâtnostej i ee primeneniâ, Tome 22 (1977) no. 2, pp. 429-435
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The representation
\begin{equation}
x(t)=\sum_{n=1}^N\int_{-\infty}^tF_n(t,u)\,dz_n(u)
\end{equation}
of a second order stochastic process $x(t)$, $t\in R^1$, is considered as a sum of representations for $N$ mutually orthogonal processes
\begin{equation}
x_n(t)=\int_{-\infty}^tF_n(t,u)\,dz_n(u).
\end{equation}
Conditions are given under which representation (1) is canonical or proper canonical (in T. Hida's terminology). These conditions are formulated in terms of the processes $x_1,\dots,x_N$ and their representations (2).
@article{TVP_1977_22_2_a23,
author = {T. N. Siraya},
title = {Canonical representations of second order stochastic processes},
journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
pages = {429--435},
publisher = {mathdoc},
volume = {22},
number = {2},
year = {1977},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/TVP_1977_22_2_a23/}
}
T. N. Siraya. Canonical representations of second order stochastic processes. Teoriâ veroâtnostej i ee primeneniâ, Tome 22 (1977) no. 2, pp. 429-435. http://geodesic.mathdoc.fr/item/TVP_1977_22_2_a23/