### Abstract

Original language | English (US) |
---|---|

Article number | 1310.6023 |

Journal | arXiv |

State | Published - Oct 22 2013 |

### Fingerprint

### Keywords

- math.PR
- math.AP
- math.DS
- 60J60, 35J15, 35F21

### Cite this

*arXiv*, [1310.6023].

**Scaling limits for conditional diffusion exit problems, Doob's h-transform, and asymptotics for nonlinear elliptic equations.** / Bakhtin, Yury; Swiech, Andrzej.

Research output: Contribution to journal › Article

}

TY - JOUR

T1 - Scaling limits for conditional diffusion exit problems, Doob's h-transform, and asymptotics for nonlinear elliptic equations

AU - Bakhtin, Yury

AU - Swiech, Andrzej

N1 - 41 pages

PY - 2013/10/22

Y1 - 2013/10/22

N2 - 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 problem to the Levinson case. We devote a separate section to a rigorous and general discussion of h-transform.

AB - 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 problem to the Levinson case. We devote a separate section to a rigorous and general discussion of h-transform.

KW - math.PR

KW - math.AP

KW - math.DS

KW - 60J60, 35J15, 35F21

M3 - Article

JO - arXiv

JF - arXiv

M1 - 1310.6023

ER -