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Quasi-diffusion solution of a stochastic differential equation

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Plucińska A., Szymański W.

Applicationes Mathematicae

2007

tom 34

nr 2

205-213

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.

Ograniczanie wyników

1 Applicationes Mathematicae

1 Plucińska A.

1 Szymański W.

1 2007

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Quasi-diffusion solution of a stochastic differential equation