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arXiv · 2309.09551

A Generalized Rough Super Brownian Motion

Ruhong Jin
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Abstract

In this paper, we construct scaling limits of some branching random walks in random environment whose off-spring distributions have infinite variance. The Laplace functional of the obtained random measure is given by a non-linear PAM, whose existence and uniqueness are also proved as an intermediate step. We also give a martingale characterization of above super-process and show that it possesses the compact support property and exponential persisitency.

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Ruhong Jin. 2023-09-18. A Generalized Rough Super Brownian Motion. https://arxiv.org/abs/2309.09551

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