Teoriâ veroâtnostej i ee primeneniâ, Tome 25 (1980) no. 3, pp. 606-613
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G. L. Kulinič; Le Thieng Huong. On the construction and limit behaviour of a multiple stochastic integral for the diffusion process. Teoriâ veroâtnostej i ee primeneniâ, Tome 25 (1980) no. 3, pp. 606-613. http://geodesic.mathdoc.fr/item/TVP_1980_25_3_a16/
@article{TVP_1980_25_3_a16,
author = {G. L. Kulini\v{c} and Le Thieng Huong},
title = {On the construction and limit behaviour of a~multiple stochastic integral for the diffusion process},
journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
pages = {606--613},
year = {1980},
volume = {25},
number = {3},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/TVP_1980_25_3_a16/}
}
TY - JOUR
AU - G. L. Kulinič
AU - Le Thieng Huong
TI - On the construction and limit behaviour of a multiple stochastic integral for the diffusion process
JO - Teoriâ veroâtnostej i ee primeneniâ
PY - 1980
SP - 606
EP - 613
VL - 25
IS - 3
UR - http://geodesic.mathdoc.fr/item/TVP_1980_25_3_a16/
LA - ru
ID - TVP_1980_25_3_a16
ER -
%0 Journal Article
%A G. L. Kulinič
%A Le Thieng Huong
%T On the construction and limit behaviour of a multiple stochastic integral for the diffusion process
%J Teoriâ veroâtnostej i ee primeneniâ
%D 1980
%P 606-613
%V 25
%N 3
%U http://geodesic.mathdoc.fr/item/TVP_1980_25_3_a16/
%G ru
%F TVP_1980_25_3_a16
We give the definition of the multiple integral $$ I_f=\int_0^T\dotsi\int_0^Tf(\xi(t_1),\dots,\xi(t_m))\,d\xi(t_1)\dots d\xi(t_m) $$ where $\xi(t)$ is the solution of the Ito's diffusion equation $$ d\xi(t)=a(t,\xi(t))\,dt+\sigma(t,\xi(t))\,dw(t). $$ The asymptotic distributions of the integral $I_t$ are investigated.
