GAUGE THEOREMS FOR RESOLVENTS WITH APPLICATION TO MARKOV-PROCESSES

• 成果类型: Article
• 署名作者: STURM, KT
• 刊物名称: PROBABILITY THEORY AND RELATED FIELDS
• ISSN/ISSBN: 0178-8051
• DOI: 10.1007/BF01199785
• 发表日期: 1991
• 页码: 387-406
• 关键词: conditional gauge; schrodinger operator; functionals; potentials

摘要

Let V = (V-alpha)-alpha greater-than-or-equal-to 0 be a (not necessarily sub-Markovian) resolvent such that the kernel V-alpha for some alpha greater-than-or-equal-to 0 is compact and irreducible. We prove the following general gauge theorem: If there exists at least one V-excessive function which is not V-invariant, then V0 is bounded. This result will be applied to resolvents U(M) arising from perturbation of sub-Markovian right resolvents U by multiplicative functionals M (not necessarily supermartingale), for instance, by Feynman-Kac functionals. Among others, this leads to an extension of the gauge theorem of Chung/Rao and even of one direction of the conditional gauge theorem of Falkner and Zhao.