OPTIMAL LOCAL HOLDER INDEX FOR DENSITY STATES OF SUPERPROCESSES WITH (1+β)-BRANCHING MECHANISM

• 成果类型: Article
• 署名作者: Fleischmann, Klaus; Mytnik, Leonid; Wachtel, Vitali
• 署名单位: Technion Israel Institute of Technology; University of Munich
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/09-AOP501
• 发表日期: 2010
• 页码: 1180-1220
• 关键词: partial-differential equations; super-brownian motion; driven; REGULARITY; noise

摘要

For 0 < alpha <= 2, a super-alpha-stable motion X in R(d) with branching of index 1 + beta is an element of (1,2) is considered. Fix arbitrary t > 0. If d < alpha/beta, a dichotomy for the density function of the measure X(t) holds: the density function is locally Holder continuous if d = 1 and alpha > 1 + beta but locally unbounded otherwise. Moreover, in the case of continuity, we determine the optimal local Holder index.