R2上粗糙超布朗运动的紧致支撑性质

IF 1.1 2区数学 Q3 STATISTICS & PROBABILITY

Stochastic Processes and their Applications Pub Date : 2025-01-15 DOI:10.1016/j.spa.2025.104568

Ruhong Jin , Nicolas Perkowski

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引用次数: 0

摘要

我们讨论了Perkowski和Rosati（2021）构建的粗糙超布朗运动的紧支撑特性作为静态随机环境下分支随机游走的尺度极限。与这个测度值过程相对应的半线性方程是连续抛物型安德森模型，这是一个需要重新规范化的奇异SPDE，这阻止了像Englander（2006）那样使用经典PDE参数。但在Moinat（2020）开发的内部估计方法的帮助下，我们能够证明紧凑支撑特性也适用于粗糙的超布朗运动。

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The compact support property of rough super Brownian motion on R2

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.

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来源期刊

Stochastic Processes and their Applications 数学-统计学与概率论

CiteScore

2.90

自引率

7.10%

发文量

180

审稿时长

23.6 weeks

期刊介绍： Stochastic Processes and their Applications publishes papers on the theory and applications of stochastic processes. It is concerned with concepts and techniques, and is oriented towards a broad spectrum of mathematical, scientific and engineering interests. Characterization, structural properties, inference and control of stochastic processes are covered. The journal is exacting and scholarly in its standards. Every effort is made to promote innovation, vitality, and communication between disciplines. All papers are refereed.