Approximate exit probabilities for a Brownian bridge on a short time interval, and applications

Authors
Lerche, H. R. Siegmund, D.
Citation
R. Lerche, H. et D. Siegmund,, Approximate exit probabilities for a Brownian bridge on a short time interval, and applications, Advances in applied probability , 21(1), 1989, pp. 1-19
Journal title
Advances in applied probability → ACNP
ISSN journal
00018678
Volume
21
Issue
1
Year of publication
1989
Pages
1 - 19
Database
ACNP
SICI code
Abstract
Let T be the first exit time of Brownian motion W(t) from a region . in d-dimensional Euclidean space having a smooth boundary. Given points .0 and .1 in ., ordinary and large-deviation approximations are given for Pr{T < . |W(0) = .0, W(.) = . 1} as . . 0. Applications are given to hearing the shape of a drum and approximating the second virial coefficient.