We consider the stochastic differential equation
$$
X_t=X_0+\int_0^t\,(A_s+B_s X_s) \,ds + \int_0^t C_s\,dY_s,
$$
where $A_t$, $B_t$, $C_t$ are nonrandom continuous functions of
$t$,
$X_0$ is an initial random variable, $Y=(Y_t,\,t\geq 0)$ is a
Gaussian process and $X_0$, $Y$ are independent.
We give the form of the solution ($X_t$) to (0.1)
and then basing on the results of Pluci/nska [Teor. Veroyatnost. i Primenen. 25 (1980)]
we prove
that ($X_t$) is a quasi-diffusion proces.
Keywords:
consider stochastic differential equation int s int where nonrandom continuous functions initial random variable geq gaussian process independent form solution basing results pluci nska teor veroyatnost primenen prove quasi diffusion proces
Affiliations des auteurs :
Agnieszka Pluci/nska
1
;
Wojciech Szyma/nski
1
1
Faculty of Mathematics and Information Science Warsaw University of Technology Pl. Politechniki 1, room 228 00-661 Warszawa, Poland
@article{10_4064_am34_2_5,
author = {Agnieszka Pluci/nska and Wojciech Szyma/nski},
title = {Quasi-diffusion solution of a stochastic differential equation},
journal = {Applicationes Mathematicae},
pages = {205--213},
year = {2007},
volume = {34},
number = {2},
doi = {10.4064/am34-2-5},
zbl = {1121.60063},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.4064/am34-2-5/}
}
TY - JOUR
AU - Agnieszka Pluci/nska
AU - Wojciech Szyma/nski
TI - Quasi-diffusion solution of a stochastic differential equation
JO - Applicationes Mathematicae
PY - 2007
SP - 205
EP - 213
VL - 34
IS - 2
UR - http://geodesic.mathdoc.fr/articles/10.4064/am34-2-5/
DO - 10.4064/am34-2-5
LA - en
ID - 10_4064_am34_2_5
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%A Wojciech Szyma/nski
%T Quasi-diffusion solution of a stochastic differential equation
%J Applicationes Mathematicae
%D 2007
%P 205-213
%V 34
%N 2
%U http://geodesic.mathdoc.fr/articles/10.4064/am34-2-5/
%R 10.4064/am34-2-5
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%F 10_4064_am34_2_5
Agnieszka Pluci/nska; Wojciech Szyma/nski. Quasi-diffusion solution of a stochastic differential equation. Applicationes Mathematicae, Tome 34 (2007) no. 2, pp. 205-213. doi: 10.4064/am34-2-5
