Asymptotics for the principal eigenvalue and eigenfunction of a nearly first-order operator with large potential

• 成果类型: Article
• 署名作者: Fleming, WH; Sheu, SJ
• 署名单位: Brown University; Academia Sinica - Taiwan
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/aop/1023481117
• 发表日期: 1997
• 页码: 1953-1994
• 关键词: markov process expectations; large time; ergodic control; series

摘要

The asymptotic behaviors of the principal eigenvalue and the corresponding normalized eigenfunction of the operator G(epsilon) f = (epsilon/2)Delta f + g del f + (l/epsilon)f for Small epsilon are studied. Under some conditions, the first order expansions for them are obtained. Two applications to risk-sensitive control problems are also mentioned.