## The Annals of Probability

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

Paolo Baldi

#### 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

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

Digital Object Identifier
doi:10.1214/aop/1176987797

Mathematical Reviews number (MathSciNet)
MR1379162

Zentralblatt MATH identifier
0856.60033

JSTOR