Quasi-diffusion solution of a stochastic differential equation

• Autorzy: Agnieszka Plucińska , Wojciech Szymański
• Języki publikacji: EN

Abstrakty

EN

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.

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Applicationes Mathematicae
• Rocznik: 2007
• Tom: 34
• Numer: 2
• Strony: 205-213

Daty

wydano

2007

Twórcy

autor

Agnieszka Plucińska

• Faculty of Mathematics and Information Science, Warsaw University of Technology, Pl. Politechniki 1, room 228, 00-661 Warszawa, Poland

autor

Wojciech Szymański

• Faculty of Mathematics and Information Science, Warsaw University of Technology, Pl. Politechniki 1, room 228, 00-661 Warszawa, Poland

Identyfikatory

DOI

10.4064/am34-2-5