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

作     者：Zhen-Qing Chen Yan-Xia Ren Renming Song 

作者机构：Department of Mathematics University of Washington Seattle WA 98195 USA LMAM School of Mathematical Sciences & Center for Statistical SciencePeking University Beijing 100871 China Department of Mathematics University of Illinois Urbana IL 61801 USA 

出 版 物：《Science China Mathematics》 (中国科学：数学（英文版）)

年 卷 期：2019年第62卷第8期

页      面：1439-1462页

核心收录：

学科分类：07[理学] 0701[理学-数学] 070101[理学-基础数学] 

基　　金：supported by Simons Foundation (Grant No. 520542) a Victor Klee Faculty Fellowship and National Natural Science Foundation of China (Grant No. 11731009) supported by National Natural Science Foundation of China (Grant Nos. 11671017 and 11731009) Key Laboratory of Mathematical Economics and Quantitative Finance (LMEQF) (Peking University),Ministry of Education supported by the Simons Foundation (Grant No. #429343) 

主　　题：multitype superdiffusion non-local branching mechanism switched diffusion spine decomposition martingale 

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.