Kolmogorov's test for super-Brownian motion

• 成果类型: Article
• 署名作者: Dhersin, JS; Le Gall, JF
• 署名单位: Universite Paris Cite; Universite PSL; Ecole Normale Superieure (ENS)
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• 发表日期: 1998
• 页码: 1041-1056
• 关键词: differential-equations; path properties; superprocesses; snake

摘要

We prove a Kolmogorov test for super-Brownian motion started at the Dirac mass at the origin. More precisely, we determine the functions g such that for all t small enough, the support of the process at time t will be contained in the ball of radius g(t) centered at 0. As a consequence, we get a necessary and sufficient condition for the existence in certain spacetime domains of a solution of the associated semilinear partial differential equation that blows up at the origin.