ASYMPTOTIC SERIES AND EXIT TIME PROBABILITIES

• 成果类型: Article
• 署名作者: FLEMING, WH; JAMES, MR
• 署名单位: University of Kentucky
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/aop/1176989695
• 发表日期: 1992
• 页码: 1369-1384
• 关键词: vanishing viscosity; stochastic control

摘要

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 cor-responding Hamilton-Jacobi PDE of first order.