## The Annals of Probability

- Ann. Probab.
- Volume 23, Number 4 (1995), 1644-1670.

### Exact Asymptotics for the Probability of Exit from a Domain and Applications to Simulation

#### Abstract

We study the asymptotics of the exit probability $\mathbb{P}^\varepsilon_{x,s}\{\tau \leq T\}$, where $\tau$ is the exit time from an open set and $\mathbb{P}^\varepsilon_{x,s}$ is the law of a diffusion process with a small parameter $\varepsilon$ multiplying the diffusion coefficient. We consider the case of the Brownian bridge in many dimensions, this choice being motivated by applications to numerical simulation. The method uses recent results reducing the problem to the solution of a system of linear first-order PDE's.

#### Article information

**Source**

Ann. Probab., Volume 23, Number 4 (1995), 1644-1670.

**Dates**

First available in Project Euclid: 19 April 2007

**Permanent link to this document**

https://projecteuclid.org/euclid.aop/1176987797

**Digital Object Identifier**

doi:10.1214/aop/1176987797

**Mathematical Reviews number (MathSciNet)**

MR1379162

**Zentralblatt MATH identifier**

0856.60033

**JSTOR**

links.jstor.org

**Subjects**

Primary: 60F10: Large deviations

Secondary: 60J60: Diffusion processes [See also 58J65] 60J65: Brownian motion [See also 58J65]

**Keywords**

Large deviations exact asymptotics Brownian bridge

#### Citation

Baldi, Paolo. Exact Asymptotics for the Probability of Exit from a Domain and Applications to Simulation. Ann. Probab. 23 (1995), no. 4, 1644--1670. doi:10.1214/aop/1176987797. https://projecteuclid.org/euclid.aop/1176987797