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

Yuri Bakhtin, Andrzej Święch

Research output: Contribution to journalArticle

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.

Original languageEnglish (US)
Pages (from-to)6487-6517
Number of pages31
JournalTransactions of the American Mathematical Society
Volume368
Issue number9
DOIs
StatePublished - 2016

Fingerprint

H-transform
Exit Problem
Nonlinear Elliptic Equations
Scaling Limit
Diffusion Problem
Mathematical transformations
Convergence Estimates
Gradient Estimate
Asymptotic Convergence
Large Deviation Principle
Nonlinear equations
Conditioning
Central limit theorem
Diffusion Process

Keywords

  • Diffusion
  • Doob’s h- transform
  • Elliptic PDE
  • Exit problems
  • Hamilton-Jacobi-Bellman equation
  • Region of strong regularity
  • Scaling limit
  • Small noise
  • Viscosity solution

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics

Cite this

Scaling limits for conditional diffusion exit problems and asymptotics for nonlinear elliptic equations. / Bakhtin, Yuri; Święch, Andrzej.

In: Transactions of the American Mathematical Society, Vol. 368, No. 9, 2016, p. 6487-6517.

Research output: Contribution to journalArticle

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