Regularity and irregularity of (1+β)-stable super-Brownian motion

• 成果类型: Article
• 署名作者: Mytnik, L; Perkins, E
• 署名单位: Technion Israel Institute of Technology; University of British Columbia
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• 发表日期: 2003
• 页码: 1413-1440
• 关键词: partial-differential equations; diffusion; driven

摘要

This paper establishes the continuity of the density of (1 + beta)-stable super-Brownian motion (0 < beta < 1) for fixed times in d = 1, and local unboundedness of the density in all higher dimensions where it exists. We also prove local unboundedness of the density in time for a fixed spatial parameter in any dimension where the density exists, and local unboundedness of the occupation density (the local time) in the spatial parameter for dimensions d greater than or equal to 2 where the local time exists.