Stochastic integral representation and regularity of the density for the exit measure of super-Brownian motion

• 成果类型: Article
• 署名作者: Le Gall, JF; Mytnik, L
• 署名单位: Universite PSL; Ecole Normale Superieure (ENS); Technion Israel Institute of Technology
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/009117904000000612
• 发表日期: 2005
• 页码: 194-222
• 关键词: boundary

摘要

This paper studies the regularity properties of the density of the exit measure for super-Brownian motion with (1 + beta)-stable branching mechanism. It establishes the continuity of the density in dimension d = 2 and the unboundedness of the density in all other dimensions where the density exists. An alternative description of the exit measure and its density is also given via a stochastic integral representation. Results are applied to the probabilistic representation of nonnegative solutions of the partial differential equation Deltau = u(1 + beta).