Fourier series expansion of stochastic measures
Teoriâ veroâtnostej i ee primeneniâ, Tome 63 (2018) no. 2, pp. 389-401
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We consider processes of the form $\mu(t)=\mu((0,t])$, where $\mu$ is a
$\sigma$-additive in probability stochastic set function. Convergence of
a random Fourier series to $\mu(t)$ is proved, and the approximation of
integrals with respect to $\mu$ using Fejèr sums is obtained. For this
approximation, we prove the convergence of solutions of the heat equation driven
by $\mu$.
Keywords:
stochastic measure, random Fourier series, stochastic integral, stochastic heat equation, mild solution.
@article{TVP_2018_63_2_a7,
author = {V. M. Radchenko},
title = {Fourier series expansion of stochastic measures},
journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
pages = {389--401},
publisher = {mathdoc},
volume = {63},
number = {2},
year = {2018},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/TVP_2018_63_2_a7/}
}
V. M. Radchenko. Fourier series expansion of stochastic measures. Teoriâ veroâtnostej i ee primeneniâ, Tome 63 (2018) no. 2, pp. 389-401. http://geodesic.mathdoc.fr/item/TVP_2018_63_2_a7/