Interacting superprocesses with discontinuous spatial motion
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Zhen-Qing Chen
,
Hao Wang
Abstract.
A class of interacting superprocesses arising from branching particle systems with continuous spatial motions, called superprocesses with dependent spatial motion (SDSMs), has been introduced and studied by Wang and by Dawson, Li and Wang. In this paper, we extend the model to allow discontinuous spatial motions. Under Lipschitz condition for coefficients, we show that under a proper rescaling, branching particle systems with jump-diffusion underlying motions in a random medium converge to a measure-valued process, called stable SDSM. We further characterize this stable SDSM as a unique solution of a well-posed martingale problem. To prove the uniqueness of the martingale problem, we establish the C2+γ-regularity for the transition semigroup of a class of jump-diffusion processes, which may be of independent interest.
© 2012 by Walter de Gruyter Berlin Boston
Artikel in diesem Heft
- Masthead
- Generalized pseudohermitian manifolds
- Loop space homology associated with the mod 2 Dickson invariants
- Interacting superprocesses with discontinuous spatial motion
- Jacobsthal identity for
- Regularized theta lift and formulas of Katok–Sarnak type
- Holomorphic extensions associated with series expansions
- Stone duality for real-valued multisets
- Corrigendum: Some characterizations of finite groups in which semipermutability is a transitive relation [Forum Math.22 (2010), 855–862]
Artikel in diesem Heft
- Masthead
- Generalized pseudohermitian manifolds
- Loop space homology associated with the mod 2 Dickson invariants
- Interacting superprocesses with discontinuous spatial motion
- Jacobsthal identity for
- Regularized theta lift and formulas of Katok–Sarnak type
- Holomorphic extensions associated with series expansions
- Stone duality for real-valued multisets
- Corrigendum: Some characterizations of finite groups in which semipermutability is a transitive relation [Forum Math.22 (2010), 855–862]
