Teoriâ veroâtnostej i ee primeneniâ, Tome 12 (1967) no. 3, pp. 548-551
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G. L. Kulinich. On the limit behaviour of the solution of a stochastic diffusion equation. Teoriâ veroâtnostej i ee primeneniâ, Tome 12 (1967) no. 3, pp. 548-551. http://geodesic.mathdoc.fr/item/TVP_1967_12_3_a13/
@article{TVP_1967_12_3_a13,
author = {G. L. Kulinich},
title = {On the limit behaviour of the solution of a~stochastic diffusion equation},
journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
pages = {548--551},
year = {1967},
volume = {12},
number = {3},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/TVP_1967_12_3_a13/}
}
TY - JOUR
AU - G. L. Kulinich
TI - On the limit behaviour of the solution of a stochastic diffusion equation
JO - Teoriâ veroâtnostej i ee primeneniâ
PY - 1967
SP - 548
EP - 551
VL - 12
IS - 3
UR - http://geodesic.mathdoc.fr/item/TVP_1967_12_3_a13/
LA - ru
ID - TVP_1967_12_3_a13
ER -
%0 Journal Article
%A G. L. Kulinich
%T On the limit behaviour of the solution of a stochastic diffusion equation
%J Teoriâ veroâtnostej i ee primeneniâ
%D 1967
%P 548-551
%V 12
%N 3
%U http://geodesic.mathdoc.fr/item/TVP_1967_12_3_a13/
%G ru
%F TVP_1967_12_3_a13
The probability density of the limit distribution of the process $f(\xi(tT))/\sqrt T$ as $T\to\infty$ is found where $$ f(x)=\int_0^x\exp\biggl\{-2\int_{-\infty}^y\biggl[\frac{a(u)}{\sigma^2(u)}-\frac12\frac{\sigma'(u)}{\sigma(u)}\biggr]\,du\biggr\}\frac{dy}{\sigma(y)}, $$ and $\xi(t)$ is the solution of stochastic diffusion equation (1).
