Superprocess Approximation for a Spati- Ally Homogeneous Branching Walk
نویسنده
چکیده
We present an alternative particle picture for super-stable motion. It is based on a non-local branching mechanism in discrete time and only trivial space motion.
منابع مشابه
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...
متن کاملCentral Limit Theorem in Multitype Branching Random Walk
A discrete time multitype (p-type) branching random walk on the real line R is considered. The positions of the j-type individuals in the n-th generation form a point process. The asymptotic behavior of these point processes, when the generation size tends to infinity, is studied. The central limit theorem is proved.
متن کاملALMOST SURE FINITENESS FOR THE TOTAL OCCUPATION TIME OF AN (d,α,β)-superprocess
For 0 < α ≤ 2 and 0 < β ≤ 1 the (d,α,β)-superprocess is the superprocess with symmetric α-stable spatial movement in Rd and spectrally positive (1+β)-stable branching. It is a measurevalued process arising as the high density limit of empirical measure for the following critical branching symmetric α-stable particle system. Independent of the others, each particle is assigned a mass n−1 and it ...
متن کاملA superprocess involving both branching and coalescing
Abstract We consider a superprocess with coalescing Brownian spatial motion. We first prove a dual relationship between two systems of coalescing Brownian motions. In consequence we can express the Laplace functionals for the superprocess in terms of coalescing Brownian motions, which allows us to obtain some explicit results. We also point out several connections between such a superprocess an...
متن کاملContinuous local time of a purely atomic immigration superprocess with dependent spatial motion
A purely atomic immigration superprocess with dependent spatial motion in the space of tempered measures is constructed as the unique strong solution of a stochastic integral equation driven by Poisson processes based on the excursion law of a Feller branching diffusion, which generalizes the work of Dawson and Li [3]. As an application of the stochastic equation, it is proved that the superpro...
متن کامل