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.
| Original language | English |
|---|---|
| Pages (from-to) | 1439-1462 |
| Number of pages | 24 |
| Journal | Science China Mathematics |
| Volume | 62 |
| Issue number | 8 |
| DOIs | |
| Publication status | Published - 1 Aug 2019 |
| Externally published | Yes |
Keywords
- 60F15
- 60J25
- 60J80
- martingale
- multitype superdiffusion
- non-local branching mechanism
- spine decomposition
- switched diffusion
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Chen, Z. Q., Ren, Y. X., & Song, R. (2019). L log L criterion for a class of multitype superdiffusions with non-local branching mechanisms. Science China Mathematics, 62(8), 1439-1462. https://doi.org/10.1007/s11425-017-9294-9