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

• 来源期刊: 中国科学：数学（英文版）
• 年，卷（期）: 2019,（8）
• 页码范围: 1439-1462
• 页数: 24页
• 语种: 英文

摘要

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 the L log L criterion) 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.