On the behaviour of the solution of the stochastic diffusion equation in case of unbounded growth of the drift coefficient on a finite segment. (Russian) Zbl 0672.60057

Almazov, M.

Teor. Veroyatn. Mat. Stat., Kiev 39, 3-4 (1988).

The paper gives the transient probability of the limit process to which the diffusion process \(\xi_ n\) converges in the sense of finite- dimensional distributions. The diffusion process \(\xi_ n\) has the drift coefficient \(a_ n(x)=\alpha_ nI_{[a,b]}(x)\), \(a<b\), \(\alpha_ n\uparrow \infty\), and the diffusion coefficient is equal to 1.

Reviewer: L.Gal’chuk

MSC:

60H10	Stochastic ordinary differential equations (aspects of stochastic analysis)
60J60	Diffusion processes
60F15	Strong limit theorems

Keywords:

convergence of finite-dimensional distributions; diffusion process