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

@article{Bakhtin2015ScalingLF,
  title={Scaling limits for conditional diffusion exit problems and asymptotics for nonlinear elliptic equations},
  author={Yuri Bakhtin and Andrzej Swiech},
  journal={Transactions of the American Mathematical Society},
  year={2015},
  volume={368},
  pages={6487-6517}
}
  • Yuri Bakhtin, A. Swiech
  • Published 22 December 2015
  • Mathematics
  • Transactions of the American Mathematical Society
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. 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… 
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Citation Type

Universal Statistics of Incubation Periods and Other Detection Times via Diffusion Models
  • Yuri Bakhtin
  • Computer Science
    Bulletin of mathematical biology
  • 2019
TLDR
The character of the models allows us to argue that the features of the exit time distributions that are described are universal and manifest themselves in various other situations where the times involved can be described as detection or halting times, for example response times studied in psychology.

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