On the convergence of diffusion processes conditioned to remain in a bounded region for large time to limiting positive recurrent diffusion processes. (English) Zbl 0567.60076

Pinsky, Ross G.

Ann. Probab. 13, 363-378 (1985).

Diffusion processes on \({\mathbb{R}}^ d\) are considered, whose infinitesimal variance matrices are differentiable and positive, and whose drift vectors vary continuously. The paper studies the asymptotic law of such a diffusion when conditioned to remain in a bounded open set for the time interval [0,T] where T is large. The large deviation theory of Donsker and Varadhan is used to show that under suitable conditions the limit law is a positive-recurrent diffusion on G. Three simple examples are discussed.

Reviewer: Wilfrid S.Kendall

MSC:

60J60	Diffusion processes
60F10	Large deviations

Keywords:

conditioned diffusion processes; large deviation theory of Donsker and Varadhan; positive-recurrent diffusion