Quasi-diffusion solution of a stochastic differential equation

Agnieszka Plucińska, and Wojciech Szymański. "Quasi-diffusion solution of a stochastic differential equation." Applicationes Mathematicae 34.2 (2007): 205-213. <http://eudml.org/doc/279800>.

@article{AgnieszkaPlucińska2007,
abstract = {We consider the stochastic differential equation $X_t = X₀ + ∫_0^t (A_s + B_s X_s)ds + ∫_0^t C_s dY_s$, where $A_t$, $B_t$, $C_t$ are nonrandom continuous functions of t, X₀ is an initial random variable, $Y = (Y_t, t ≥ 0)$ is a Gaussian process and X₀, Y are independent. We give the form of the solution ($X_t$) to (0.1) and then basing on the results of Plucińska [Teor. Veroyatnost. i Primenen. 25 (1980)] we prove that ($X_t$) is a quasi-diffusion proces.},
author = {Agnieszka Plucińska, Wojciech Szymański},
journal = {Applicationes Mathematicae},
keywords = {quasi-diffusion process; stochastic differential equation},
language = {eng},
number = {2},
pages = {205-213},
title = {Quasi-diffusion solution of a stochastic differential equation},
url = {http://eudml.org/doc/279800},
volume = {34},
year = {2007},
}

TY - JOUR
AU - Agnieszka Plucińska
AU - Wojciech Szymański
TI - Quasi-diffusion solution of a stochastic differential equation
JO - Applicationes Mathematicae
PY - 2007
VL - 34
IS - 2
SP - 205
EP - 213
AB - We consider the stochastic differential equation $X_t = X₀ + ∫_0^t (A_s + B_s X_s)ds + ∫_0^t C_s dY_s$, where $A_t$, $B_t$, $C_t$ are nonrandom continuous functions of t, X₀ is an initial random variable, $Y = (Y_t, t ≥ 0)$ is a Gaussian process and X₀, Y are independent. We give the form of the solution ($X_t$) to (0.1) and then basing on the results of Plucińska [Teor. Veroyatnost. i Primenen. 25 (1980)] we prove that ($X_t$) is a quasi-diffusion proces.
LA - eng
KW - quasi-diffusion process; stochastic differential equation
UR - http://eudml.org/doc/279800
ER -