@article{af09aee4a18e4371874a1032d2f83087,
title = "L log L criterion for a class of multitype superdiffusions with non-local branching mechanisms",
abstract = "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.",
keywords = "60F15, 60J25, 60J80, martingale, multitype superdiffusion, non-local branching mechanism, spine decomposition, switched diffusion",
author = "Chen, {Zhen Qing} and Ren, {Yan Xia} and Renming Song",
note = "Funding Information: Zhen-Qing Chen was supported by Simons Foundation (Grant No. 520542), a Victor Klee Faculty Fellowship and National Natural Science Foundation of China (Grant No. 11731009). Yan-Xia Ren was supported by National Natural Science Foundation of China (Grant Nos. 11671017 and 11731009) and Key Laboratory of Mathematical Economics and Quantitative Finance (LMEQF) (Peking University), Ministry of Education. Renming Song was supported by the Simons Foundation (Grant No. #429343). The authors thank the referees for helpful comments on the first version of this paper. Funding Information: Zhen-Qing Chen was supported by Simons Foundation (Grant No. 520542), a Victor Klee Faculty Fellowship and National Natural Science Foundation of China (Grant No. 11731009). Yan-Xia Ren was supported by National Natural Science Foundation of China (Grant Nos. 11671017 and 11731009) and Key Laboratory of Mathematical Economics and Quantitative Finance (LMEQF) (Peking University), Ministry of Education. Renming Song was supported by the Simons Foundation (Grant No. #429343). The authors thank the referees for helpful comments on the first version of this paper. Publisher Copyright: {\textcopyright} 2019, Science China Press and Springer-Verlag GmbH Germany, part of Springer Nature.",
year = "2019",
month = aug,
day = "1",
doi = "10.1007/s11425-017-9294-9",
language = "English (US)",
volume = "62",
pages = "1439--1462",
journal = "Science China Mathematics",
issn = "1674-7283",
publisher = "Science in China Press",
number = "8",
}