Open Access
July, 1992 Asymptotic Series and Exit Time Probabilities
W. H. Fleming, M. R. James
Ann. Probab. 20(3): 1369-1384 (July, 1992). DOI: 10.1214/aop/1176989695


This paper is concerned with accurate asymptotic estimates for exit time probabilities associated with nearly deterministic Markov diffusions. The exit time probabilities are expressed as asymptotic series of WKB type in a small parameter, which measures the strength of the random Brownian motion inputs. This series is valid in certain regions in which the minimum action function $u(x,s)$ is a smooth function of state $x$ and time $s$. The function $u$ is a solution to the corresponding Hamilton-Jacobi PDE of first order.


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W. H. Fleming. M. R. James. "Asymptotic Series and Exit Time Probabilities." Ann. Probab. 20 (3) 1369 - 1384, July, 1992.


Published: July, 1992
First available in Project Euclid: 19 April 2007

zbMATH: 0771.60055
MathSciNet: MR1175266
Digital Object Identifier: 10.1214/aop/1176989695

Primary: 60F10
Secondary: 35C20

Keywords: exit time probabilities , large deviations , WKB asymptotic series

Rights: Copyright © 1992 Institute of Mathematical Statistics

Vol.20 • No. 3 • July, 1992
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