Superprocesses with spatial interactions in a random medium

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,...

Spatial Beta Regression Model with Random Effect

 Abstract: In many applications we have to encountered with bounded dependent variables. Beta regression model can be used to deal with these kinds of response variables. In this paper we aim to study spatially correlated responses in the unit interval. Initially we introduce spatial beta generalized linear mixed model in which the spatial correlation is captured through a random effect. T...

Immigration Superprocesses with Dependent Spatial Motion and Non-critical Branching

Superprocesses with Coalescing Brownian Spatial Motion as Large-Scale Limits

Large scale limits of interacting particle systems and measure-valued processes have been studied by many authors; see, e.g., Bojdecki and Gorostiza (1986), Cox et al. (2000), Dawson (1977), Dawson and Fleischmann (1988), Durrett and Perkins (1999), Hara and Slade (2000a,b). In particular, Dawson and Fleischmann (1988) investigated the scaling limit of a class of critical space-time branching m...

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...