Right inverses of nonsymmetric Levy processes
成果类型：
Article
署名作者：
Winkel, M
署名单位：
Sorbonne Universite; Universite Paris Cite
刊物名称：
ANNALS OF PROBABILITY
ISSN/ISSBN：
0091-1798
发表日期：
2002
页码：
382-415
关键词：
摘要：
We analyze the existence and properties of right inverses K for nonsymmetric Levy processes X, extending recent work of Evans 171 in the symmetric setting. First, both X and -X have right inverses if and only if X is recurrent and has a nontrivial Gaussian component, Our main result is then a description of the excursion measure n(Z) of the strong Markov process Z = X - L (reflected process) where L-t = inf{x > 0 : K-x > t}. Specifically, n(Z) is essentially the restriction of n(X) to the excursions starting negative. Second, when only asking for right inverses of X, a certain strength of asymmetry is needed. Millar's [9] notion of creeping turns out necessary but not sufficient for the existence of right inverses. we analyze this both in the bounded and unbounded variation case with a particular emphasis on results in terms of the Levy-Khintchine characteristics.