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

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...

Conditional Excursion Representation for a Class of Interacting Superprocesses

A class of interacting superprocesses, called superprocesses with dependent spatial motion (SDSMs), has been introduced and characterized in Wang [22] and Dawson et al. [7]. In this paper, we give a construction or an excursion representation of the non-degenerate SDSM with immigration by making use of a Poisson system associated with the conditional excursion laws of the SDSM. As pointed out i...

Immigration Superprocesses with Dependent Spatial Motion and Non-critical Branching

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,...