Teoriâ veroâtnostej i ee primeneniâ, Tome 17 (1972) no. 4, pp. 748-751
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V. A. Lebedev. On a transformation of systems of stochastic differential equations. Teoriâ veroâtnostej i ee primeneniâ, Tome 17 (1972) no. 4, pp. 748-751. http://geodesic.mathdoc.fr/item/TVP_1972_17_4_a13/
@article{TVP_1972_17_4_a13,
author = {V. A. Lebedev},
title = {On a transformation of systems of stochastic differential equations},
journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
pages = {748--751},
year = {1972},
volume = {17},
number = {4},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/TVP_1972_17_4_a13/}
}
TY - JOUR
AU - V. A. Lebedev
TI - On a transformation of systems of stochastic differential equations
JO - Teoriâ veroâtnostej i ee primeneniâ
PY - 1972
SP - 748
EP - 751
VL - 17
IS - 4
UR - http://geodesic.mathdoc.fr/item/TVP_1972_17_4_a13/
LA - ru
ID - TVP_1972_17_4_a13
ER -
%0 Journal Article
%A V. A. Lebedev
%T On a transformation of systems of stochastic differential equations
%J Teoriâ veroâtnostej i ee primeneniâ
%D 1972
%P 748-751
%V 17
%N 4
%U http://geodesic.mathdoc.fr/item/TVP_1972_17_4_a13/
%G ru
%F TVP_1972_17_4_a13
For a diffusion Markov process defined by the Ito equations (1), an $\mathfrak{F}_t$-measurable transformation defined by (3) or (4) with $G(z,t)$ and $F(x,t)$ satisfying (2) and (6) respectively is considered. The process $(z(t), y(t))$ where $z(t)=F(x(t), t)$ with $(x(t), y(t))$ defined by (1) is shown to satisfy the system (5).
