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 language | English (US) |
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Pages (from-to) | 6487-6517 |
Number of pages | 31 |
Journal | Transactions of the American Mathematical Society |
Volume | 368 |
Issue number | 9 |
DOIs | |
State | Published - 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