Quasi-diffusion solution of a stochastic differential equation
Applicationes Mathematicae, Tome 34 (2007) no. 2, pp. 205-213
Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences
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.
DOI :
10.4064/am34-2-5
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
@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 ER -
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
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