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$L\log L$ criterion for a class of multitype superdiffusions with non-local branching mechanisms (1708.08219v1)
Published 28 Aug 2017 in math.PR
Abstract: In this paper, we provide a pathwise spine decomposition for multitype superdiffusions with non-local 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 for superprocesses with purely local branching mechanisms and in Kyprianou and Palau (2016) for super Markov chains.