UNIFORM CONTROL OF LOCAL TIMES OF SPECTRALLY POSITIVE STABLE PROCESSES

• 成果类型: Article
• 署名作者: Forman, Noah; Pal, Soumik; Rizzolo, Douglas; Winkel, Matthias
• 署名单位: University of Washington; University of Washington Seattle; University of Delaware; University of Oxford
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• DOI: 10.1214/17-AAP1370
• 发表日期: 2018
• 页码: 2592-2634
• 关键词: asymmetric levy processes; ergodicity; EXIT

摘要

We establish two results about local times of spectrally positive stable processes. The first is a general approximation result, uniform in space and on compact time intervals, in a model where each jump of the stable process may be marked by a random path. The second gives moment control on the Holder constant of the local times, uniformly across a compact spatial interval and in certain random time intervals. For the latter, we introduce the notion of a Levy process restricted to a compact interval, which is a variation of Lambert's Levy process confined in a finite interval and of Pistorius' doubly reflected process. We use the results of this paper to exhibit a class of path-continuous branching processes of Crump-Mode-Jagers-type with continuum genealogical structure. A further motivation for this study lies in the construction of diffusion processes in spaces of interval partitions and R-trees, which we explore in forthcoming articles. In that context, local times correspond to branch lengths.