Spine decompositions and limit theorems for a class of critical superprocesses

Yan-Xia Ren; Renming Song; Zhenyao Sun

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arXiv · 1711.09188

Spine decompositions and limit theorems for a class of critical superprocesses

Yan-Xia Ren·Renming Song·Zhenyao Sun

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Abstract

In this paper, we first establish a decomposition theorem for size-biased Poisson random measures. As consequences of this decomposition theorem, we get a spine decomposition theorem and a 2-spine decomposition theorem for some critical superprocesses. Then we use these spine decomposition theorems to give probabilistic proofs of the asymptotic behavior of the survival probability and Yaglom's exponential limit law for critical superprocesses.

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Yan-Xia Ren, Renming Song, Zhenyao Sun. 2017-11-25. Spine decompositions and limit theorems for a class of critical superprocesses. https://arxiv.org/abs/1711.09188

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