ON THE BOUNDARY OF THE SUPPORT OF SUPER-BROWNIAN MOTION

• 成果类型: Article
• 署名作者: Mueller, Carl; Mytnik, Leonid; Perkins, Edwin
• 署名单位: University of Rochester; Technion Israel Institute of Technology; University of British Columbia
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/16-AOP1141
• 发表日期: 2017
• 页码: 3481-3534
• 关键词: heat-equation; potential-theory; subordinators; nonuniqueness; coefficients; absorption; uniqueness; noise

摘要

We study the density X(t, x) of one-dimensional super-Brownian motion and find the asymptotic behaviour of P(0 < X( t, x) <= a) as a down arrow 0 as well as the Hausdorff dimension of the boundary of the support of X(t, .). The answers are in terms of the leading eigenvalue of the Ornstein-Uhlenbeck generator with a particular killing term. This work is motivated in part by questions of pathwise uniqueness for associated stochastic partial differential equations.