Scaling limits for conditional diffusion exit problems and asymptotics for nonlinear elliptic equations
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- by Yuri Bakhtin and Andrzej Święch PDF
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Abstract:
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 and new asymptotic convergence gradient estimates for elliptic nonlinear equations that allow one to reduce the problem to the Levinson case. We devote an appendix to a rigorous and general discussion of $h$-transform.References
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Additional Information
- Yuri Bakhtin
- Affiliation: Courant Institute of Mathematical Sciences, New York University, 251 Mercer Street, New York, New York 10012
- MR Author ID: 648835
- ORCID: 0000-0003-1125-4543
- Andrzej Święch
- Affiliation: School of Mathematics, Georgia Institute of Technology, 686 Cherry Street, Atlanta, Georgia 30332-0160
- Received by editor(s): October 22, 2013
- Received by editor(s) in revised form: August 25, 2014
- Published electronically: December 22, 2015
- Additional Notes: The first author was partially supported by NSF via DMS-1407497 and CAREER DMS-0742424. The second author was partially supported by NSF grant DMS-0856485.
- © Copyright 2015 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 368 (2016), 6487-6517
- MSC (2010): Primary 60J60, 35J15, 35F21
- DOI: https://doi.org/10.1090/tran/6574
- MathSciNet review: 3461040