Immigration structures associated with Dawson-Watanabe superprocesses

Some Local Approximations of Dawson – Watanabe

Let ξ be a Dawson–Watanabe superprocess in R such that ξt is a.s. locally finite for every t ≥ 0. Then for d ≥ 2 and fixed t > 0, the singular random measure ξt can be a.s. approximated by suitably normalized restrictions of Lebesgue measure to the ε-neighborhoods of supp ξt. When d ≥ 3, the local distributions of ξt near a hitting point can be approximated in total variation by those of a stat...

Immigration Superprocesses with Dependent Spatial Motion and Non-critical Branching

Construction of Immigration Superprocesses with Dependent Spatial Motion from One-Dimensional Excursions

A superprocess with dependent spatial motion and interactive immigration is constructed as the pathwise unique solution of a stochastic integral equation carried by a stochastic flow and driven by Poisson processes of one-dimensional excursions. Mathematics Subject Classification (2000): Primary 60J80; Secondary 60G57, 60H20

Conditional Log-Laplace Functionals of Immigration Superprocesses with Dependent Spatial Motion

Conditional Log-Laplace Functionals of Immigration Superprocesses with Dependent Spatial Motion Zenghu Li a1, Hao Wang b2 and Jie Xiong c3 a School of Mathematical Sciences, Beijing Normal University, Beijing 100875, P.R. China E-mail: [email protected] b Department of Mathematics, University of Oregon, Eugene OR 97403-1222, U.S.A. E-mail: [email protected] c Department of Mathem...

Interacting Superprocesses with Discontinuous Spatial Motion and their Associated SPDEs

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 in Wang [26] and Dawson et al. [8]. In this paper, we extend the model to allow discontinuous spatial motions. Under Lipschitz condition for coefficients, we show that under a proper rescaling,...