Discontinuous Superprocesses with Dependent Spatial Motion
We construct a class of discontinuous superprocesses with dependent spatial motion and general branching mechanism. The process arises as the weak limit of critical interactingbranching particle systems where the spatial motions of the particles are not independent.The main work is to solve the martingale problem. When we turn to the uniqueness of the process, we generalize the localization method introduced by D.W. Stroock, Diffusion processes associated with L(e)vy generators, Z. Wahrscheinlichkeitstheorie und Verw. Gebiete, 32(1975)209-244 to the measure-valued context. As for existence, we use particle system approximation and a perturbation method. This work generalizes the model introduced in D.A. Dawson, Z.Li, H Wang, Superprocesses with dependent spatial motion and general branching densities,Electron. J. Probab. 6(2001), no.25, 33 pp. (electronic) where quadratic branching mechanism was considered. We also investigate some properties of the process.
measure-valued process superprocess dependent spatial motion interaction localization procedure duality martingale problem semi-martingale representation perturbation moment formula
Hui He
Laboratory of Mathematics and Complex Systems,School of Mathematical Sciences, Beijing Normal University,Beijing 100875, Peoples Republic of China
国际会议
北京
英文
38-71
2008-08-10（万方平台首次上网日期，不代表论文的发表时间）