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April, 1993 Large Deviations for Markov Processes Corresponding to PDE Systems
Alexander Eizenberg, Mark Freidlin
Ann. Probab. 21(2): 1015-1044 (April, 1993). DOI: 10.1214/aop/1176989280


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.


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Alexander Eizenberg. Mark Freidlin. "Large Deviations for Markov Processes Corresponding to PDE Systems." Ann. Probab. 21 (2) 1015 - 1044, April, 1993.


Published: April, 1993
First available in Project Euclid: 19 April 2007

zbMATH: 0776.60037
MathSciNet: MR1217578
Digital Object Identifier: 10.1214/aop/1176989280

Primary: 60F10
Secondary: 35B25 , 35J55

Keywords: large deviations , PDE systems , singular perturbations , small random perturbations

Rights: Copyright © 1993 Institute of Mathematical Statistics

Vol.21 • No. 2 • April, 1993
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