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 

机构地区：[1]Department of Mathematics, University of Washington, Seattle, WA 98195, USA [2]LMAM, School of Mathematical Sciences & Center for Statistical Science,Peking University, Beijing 100871, China [3]Department of Mathematics, University of Illinois, Urbana, IL 61801, USA

出　　处：《Science China Mathematics》2019年第8期1439-1462,共24页中国科学：数学（英文版）

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)

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.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.

关 键 词：multitype SUPERDIFFUSION NON-LOCAL branching mechanism SWITCHED diffusion SPINE decomposition MARTINGALE 

分 类 号：O1[理学—数学]