Some Local Approximations of Dawson – Watanabe
نویسندگان
چکیده
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 stationary and self-similar pseudo-random measure ξ̃. By contrast, the corresponding distributions for d= 2 are locally invariant. Further results include improvements of some classical extinction criteria and some limiting properties of hitting probabilities. Our main proofs are based on a detailed analysis of the historical structure of ξ.
منابع مشابه
Local Annihilation Method and Some Stiff Problems
In this article, a new scheme inspired from collocation method is presented for numerical solution of stiff initial-value problems and Fredholm integral equations of the first kind based on the derivatives of residual function. Then, the error analysis of this method is investigated by presenting an error bound. Numerical comparisons indicate that the presented method yields accur...
متن کاملar X iv : 0 90 1 . 02 46 v 1 [ m at h . PR ] 2 J an 2 00 9 SPATIAL EPIDEMICS AND LOCAL TIMES FOR CRITICAL BRANCHING RANDOM WALKS IN DIMENSIONS
ABSTRACT. The behavior at criticality of spatial SIR (susceptible/infected/recovered) epidemic models in dimensions two and three is investigated. In these models, finite populations of size N are situated at the vertices of the integer lattice, and infectious contacts are limited to individuals at the same or at neighboring sites. Susceptible individuals, once infected, remain contagious for o...
متن کاملComparisons for Measure Valued Processes with Interactions
This paper considers some measure-valued processes {Xt : t ∈ [0, T ]} based on an underlying critical branching particle structure with random branching rates. In the case of constant branching these processes are Dawson-Watanabe processes. Sufficient conditions on functionals Φ of the process are given that imply that the expectations E(Φ(XT )) are comparable to the constant branching case. Ap...
متن کامل$varepsilon$-Simultaneous approximations of downward sets
In this paper, we prove some results on characterization of $varepsilon$-simultaneous approximations of downward sets in vector lattice Banach spaces. Also, we give some results about simultaneous approximations of normal sets.
متن کاملAnalysis of Randomized Local Search Algorithm for LDPCC Decoding Problem
We propose an approach for analyzing the average performance of a given (randomized) local search algorithm for a constraint satisfaction problem. Our approach consists of two approximation steps. we experimentally investigate a randomized algorithm for LDPCC decoding and discuss the reliability of these approximations.
متن کامل