JUMP-TYPE HUNT PROCESSES GENERATED BY LOWER BOUNDED SEMI-DIRICHLET FORMS

• 成果类型: Article
• 署名作者: Fukushima, Masatoshi; Uemura, Toshihiro
• 署名单位: University of Osaka; Kansai University
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/10-AOP633
• 发表日期: 2012
• 页码: 858-889
• 关键词: stable-like processes; path properties

摘要

Let E be a locally compact separable metric space and in be a positive Radon measure on it. Given a nonnegative function k defined on E x E off the diagonal whose anti-symmetric part is assumed to be less singular than the symmetric part, we construct an associated regular lower bounded semi-Dirichlet form eta on L-2(E; m) producing a Hunt process X-0 on E whose jump behaviours are governed by k. For an arbitrary open subset D C E, we also construct a Hunt process X-D,X-0 on D in an analogous manner. When D is relatively compact, we show that X-D,X-0 is censored in the sense that it admits no killing inside D and killed only when the path approaches to the boundary. When E is a d-dimensional Euclidean space and In is the Lebesgue measure, a typical example of X is the stable-like process that will be also identified with the solution of a martingale problem up to an eta-polar set of starting points. Approachability to the boundary partial derivative D in finite time of its censored process X-D,X-0 on a bounded open subset D will be examined in terms of the polarity of partial derivative D for the symmetric stable processes with indices that bound the variable exponent alpha(x).