Quasi-diffusion solution of a stochastic differential equation

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

Applicationes Mathematicae, Tome 34 (2007) no. 2, pp. 205-213

Résumé

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.

Détail

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