L log L criterion for a class of multitype superdiffusions with non-local branching mechanisms
L log L criterion for a class of multitype superdiffusions with non-local branching mechanisms
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DOI：
10.1007/s11425-017-9294-9
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发表时间：
2017-08
期刊：
影响因子：
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通讯作者：
Zhen-Qing Chen;Yanxia Ren;R. Song
中科院分区：
文献类型：
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作者：
Zhen-Qing Chen;Yanxia Ren;R. Song
本文给出了测度鞅变下具有非局部分支机制的多型超扩散的路径样条分解。作为这种分解的应用，我们得到了基本鞅极限为非退化的一个充要条件（称为LlogL准则）。这一结果补充了Kyprianou et al.（2012），Kyprianou and Murillo-Salas（2013）和Liu et al.（2009）对于具有纯局部分支机制的超过程以及Kyprianou and帕劳（2018）对于超马尔可夫链的相关结果。
In this paper, we provide a pathwise spine decomposition for multitype superdiffusions with nonlocal branching mechanisms under a martingale change of measure. As an application of this decomposition, we obtain a necessary and sufficient condition (called theLlogLcriterion) for the limit of the fundamental martingale to be non-degenerate. This result complements the related results obtained in Kyprianou et al. (2012), Kyprianou and Murillo-Salas (2013) and Liu et al. (2009) for superprocesses with purely local branching mechanisms and in Kyprianou and Palau (2018) for super Markov chains.