A ROUGH SUPER-BROWNIAN MOTION

Autor(es)

Perkowski, Nicolas ^[1] ; Rosati, Tommaso ^[1]

Afiliação do(s) autor(es)

^[1] Free Univ Berlin, Inst Math, Berlin - Germany

• Tipo de documento: Artigo Científico
• Fonte: ANNALS OF PROBABILITY; v. 49, n. 2, p. 908-943, MAR 2021.
• Citações Web of Science: 0

Resumo

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. (AU)

• Processo FAPESP: 15/50122-0 - Fenômenos dinâmicos em redes complexas: fundamentos e aplicações
• Beneficiário: Elbert Einstein Nehrer Macau
• Modalidade de apoio: Auxílio à Pesquisa - Temático