Scaling limits for conditional diffusion exit problems and asymptotics for nonlinear elliptic equations

The goal of this paper is to supplement the large deviation principle of the Freidlin-Wentzell theory on exit problems for diffusion processes with results of classical central limit theorem type. Namely, we describe a class of situations where conditioning on exit through unlikely locations leads t...

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Bibliographic Details
Published in:Transactions of the American Mathematical Society 2016-09, Vol.368 (9), p.6487-6517
Main Authors: Bakhtin, Yuri, Święch, Andrzej
Format: Article
Language:English
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Summary:The goal of this paper is to supplement the large deviation principle of the Freidlin-Wentzell theory on exit problems for diffusion processes with results of classical central limit theorem type. Namely, we describe a class of situations where conditioning on exit through unlikely locations leads to a Gaussian scaling limit for the exit distribution. Our results are based on Doob's h-transform.
ISSN:0002-9947
1088-6850
DOI:10.1090/tran/6574