A ROUGH SUPER-BROWNIAN MOTION

• 成果类型: Article
• 署名作者: Perkowski, Nicolas; Rosati, Tommaso
• 署名单位: Free University of Berlin
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/20-AOP1464
• 发表日期: 2021
• 页码: 908-943
• 关键词: partial-differential equations; anderson model; superprocesses; intermittency

摘要

We study the scaling limit of a branching random walk in static random environment in dimension d = 1, 2 and show that it is given by a superBrownian motion in a white noise potential. In dimension 1 we characterize the limit as the unique weak solution to the stochastic PDE partial derivative t mu=(Delta+xi)mu+root 2 nu mu xi for independent space white noise xi and space-time white noise (xi) over tilde. In dimension 2 the study requires paracontrolled theory and the limit process is described via a martingale problem. In both dimensions we prove persistence of this rough version of the super-Brownian motion.