RECURRENT PERTURBATIONS OF CERTAIN TRANSIENT RADIALLY SYMMETRICAL DIFFUSIONS

• 成果类型: Article
• 署名作者: IOFFE, D
• 署名单位: University of California System; University of California Davis
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/aop/1176989284
• 发表日期: 1993
• 页码: 1124-1150
• 关键词: drift

摘要

If L generates a transient diffusion, then the corresponding exterior Dirichlet problem (EP) has in general many bounded solutions. We consider perturbations of L by a first-order term and assume that EP can be solved uniquely for each perturbed operator. Then as the perturbation tends to 0, the sequence of perturbed solutions may converge to a solution of the original EP. Using a skew-product representation of diffusions, we give an integral criterion for the uniqueness of this limit and show that it takes place iff the Kuramochi boundary of L at infinity is a singleton. In the case when uniqueness fails, we provide a description of a subclass of limiting solutions in terms of boundary conditions for the original process in the natural scale.