STOCHASTIC CALCULUS OVER SYMMETRIC MARKOV PROCESSES WITHOUT TIME REVERSAL

• 成果类型: Article
• 署名作者: Kuwae, Kazuhiro
• 署名单位: Kumamoto University
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/09-AOP516
• 发表日期: 2010
• 页码: 1532-1569
• 关键词: dirichlet forms

摘要

We refine stochastic calculus for symmetric Markov processes without using time reverse operators Under some conditions on the jump functions of locally square integrable martingale additive functionals, we extend Nakao's divergence-like continuous additive functional of zero energy and the stochastic integral with respect to It under the law for quasi-everywhere starting points, which are refinements of the previous results under the law for almost everywhere starting points This refinement of stochastic calculus enables us to establish a generalized Fukushima decomposition for a certain class of functions locally in the domain of Dirichlet form and a generalized Ito formula