The compact support property of rough super Brownian motion on R2

Ruhong Jin and Nicolas Perkowski

Stochastic Processes and their Applications, 2025, vol. 182, issue C

Abstract: We discuss the compact support property of the rough super-Brownian motion constructed in Perkowski and Rosati (2021) as a scaling limit of a branching random walk in static random environment. The semi-linear equation corresponding to this measure-valued process is the continuous parabolic Anderson model, a singular SPDE in need of renormalization, which prevents the use of classical PDE arguments as in Englander (2006). But with the help of an interior estimation method developed in Moinat (2020), we are able to show that the compact support property also holds for rough super-Brownian motion.

Keywords: Super-Brownian Motion; Singular Stochastic PDEs; Parabolic Anderson Model (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1016/j.spa.2025.104568

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