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.
Publié le : 1993-04-14
Classification:
Large deviations,
small random perturbations,
PDE systems,
singular perturbations,
60F10,
35B25,
35J55
@article{1176989280,
author = {Eizenberg, Alexander and Freidlin, Mark},
title = {Large Deviations for Markov Processes Corresponding to PDE Systems},
journal = {Ann. Probab.},
volume = {21},
number = {4},
year = {1993},
pages = { 1015-1044},
language = {en},
url = {http://dml.mathdoc.fr/item/1176989280}
}
Eizenberg, Alexander; Freidlin, Mark. Large Deviations for Markov Processes Corresponding to PDE Systems. Ann. Probab., Tome 21 (1993) no. 4, pp. 1015-1044. http://gdmltest.u-ga.fr/item/1176989280/