Quasi-diffusion solution of a stochastic differential equation
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.