On a~generalization of stochastic integral
Teoriâ veroâtnostej i ee primeneniâ, Tome 20 (1975) no. 2, pp. 223-238
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Let $\xi$ be a Gaussian random variable in a separable Hilbert space $H$ and $L$ be the space of random variables $\eta$ in $H$ with $\mathbf M|\eta|^2\infty$. In the paper, the integral $\langle\eta,\xi\rangle$ is introduced and its properties are investigated. If $H$ is the space of those functions $f(x)$ on a measurable space $(X,\mathfrak B)$ for which
$$
\int f^2(x)m(dx)\infty
$$
and $\mu$ is a Gaussian measure on $\mathfrak B$ with
$$
\mathbf M\mu(A)\mu(B)=m(A\cap B),
$$
then the integral
$$
\langle\eta(\,\cdot\,),\mu\rangle=\int\eta(x)\mu(dx).
$$
@article{TVP_1975_20_2_a0,
author = {A. V. Skorokhod},
title = {On a~generalization of stochastic integral},
journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
pages = {223--238},
publisher = {mathdoc},
volume = {20},
number = {2},
year = {1975},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/TVP_1975_20_2_a0/}
}
A. V. Skorokhod. On a~generalization of stochastic integral. Teoriâ veroâtnostej i ee primeneniâ, Tome 20 (1975) no. 2, pp. 223-238. http://geodesic.mathdoc.fr/item/TVP_1975_20_2_a0/