English

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

Probability 2017-08-29 v1

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 LlogLL\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.

Keywords

Cite

@article{arxiv.1708.08219,
  title  = {$L\log L$ criterion for a class of multitype superdiffusions with non-local branching mechanisms},
  author = {Zhen-Qing Chen and Yan-Xia Ren and Renming Song},
  journal= {arXiv preprint arXiv:1708.08219},
  year   = {2017}
}