## The Annals of Probability

### Large Deviations for Markov Processes Corresponding to PDE Systems

#### Abstract

We continue the study of the asymptotic behavior of Markov processes $(X^\varepsilon(t), \nu^\varepsilon(t))$ corresponding to systems of elliptic PDE with a small parameter $\varepsilon > 0$. In the present paper we consider the case where the process $(X^\varepsilon(t), \nu^\varepsilon(t))$ can leave a given domain $D$ only due to large deviations from the degenerate process $(X^0(t), \nu^0(t))$. In this way we study the limit behavior of solutions of corresponding Dirichlet problems.

#### Article information

Source
Ann. Probab., Volume 21, Number 2 (1993), 1015-1044.

Dates
First available in Project Euclid: 19 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aop/1176989280

Digital Object Identifier
doi:10.1214/aop/1176989280

Mathematical Reviews number (MathSciNet)
MR1217578

Zentralblatt MATH identifier
0776.60037

JSTOR