Additive functionals of several Levy processes and intersection local times

• 成果类型: Article
• 署名作者: Marcus, MB; Rosen, J
• 署名单位: City University of New York (CUNY) System; City College of New York (CUNY); City University of New York (CUNY) System; College of Staten Island (CUNY)
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/aop/1022874811
• 发表日期: 1999
• 页码: 1643-1678
• 关键词: symmetrical markov-processes; sample path properties

摘要

Different extensions of an isomorphism theorem of Dynkin are developed and are used to study two distinct but related families of functionals of Levy processes; n-fold near-intersections of a single Levy process and continuous additive functionals of several independent Levy processes. Intersection local times for n independent Levy processes are also studied. They are related to both of the above families. In all three cases sufficient conditions are obtained for the almost sure continuity of these functionals in terms of the almost sure continuity of associated Gaussian chaos processes. Concrete sufficient conditions are given for the almost sure continuity of these functionals of Levy processes.