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

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

Fingerprint Dive into the research topics of 'Scaling limits for conditional diffusion exit problems and asymptotics for nonlinear elliptic equations'. Together they form a unique fingerprint.

  • Cite this