• Corpus ID: 117957326

Scaling limits for conditional diffusion exit problems, Doob's h-transform, and asymptotics for nonlinear elliptic equations

  title={Scaling limits for conditional diffusion exit problems, Doob's h-transform, and asymptotics for nonlinear elliptic equations},
  author={Yuri Bakhtin and Andrzej Swiech},
  journal={arXiv: Probability},
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 kind. 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 to reduce the… 


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