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arXiv · 1708.08219

$L\log L$ criterion for a class of multitype superdiffusions with non-local branching mechanisms

Zhen-Qing Chen·Yan-Xia Ren·Renming Song
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Abstract

In this paper, we provide a pathwise spine decomposition for multitype superdiffusions with non-local branching mechanisms under a martingale change of measure. As an application of this decomposition, we obtain a necessary and sufficient condition (called the $L\log L$ criterion) for the limit of the fundamental martingale to be non-degenerate. This result complements the related results for superprocesses with purely local branching mechanisms and in Kyprianou and Palau (2016) for super Markov chains.

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Zhen-Qing Chen, Yan-Xia Ren, Renming Song. 2017-08-28. $L\log L$ criterion for a class of multitype superdiffusions with non-local branching mechanisms. https://arxiv.org/abs/1708.08219

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