Construction of immigration superprocesses with dependent spatial motion from one-dimensional excursions

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

Immigration Superprocesses with Dependent Spatial Motion and Non-critical Branching

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...

Superprocesses with Dependent Spatial Motion and General Branching Densities

Abstract We construct a class of superprocesses by taking the high density limit of a sequence of interacting-branching particle systems. The spatial motion of the superprocess is determined by a system of interacting diffusions, the branching density is given by an arbitrary bounded non-negative Borel function, and the superprocess is characterized by a martingale problem as a diffusion proces...

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,...