PERSISTENCE CRITERIA FOR A CLASS OF CRITICAL BRANCHING PARTICLE-SYSTEMS IN CONTINUOUS-TIME

• 成果类型: Article
• 署名作者: GOROSTIZA, LG; WAKOLBINGER, A
• 署名单位: Johannes Kepler University Linz
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/aop/1176990544
• 发表日期: 1991
• 页码: 266-288
• 关键词: FIELDS

摘要

We consider a system of particles in R(d) performing symmetric stable motion with exponent alpha, 0 < alpha less-than-or-equal-to 2, and branching at the end of an exponential lifetime with offspring generating function F(s) = s + 1/2(1 - s)1+beta, 0 < beta less-than-or-equal-to 1. (This includes binary branching Brownian motion for alpha = 2, beta = 1.) It is shown that, for an initial Poisson population with uniform intensity, the system goes to extinction if d less-than-or-equal-to alpha/beta and is persistent (i.e., preserves intensity in the large time limit) if d > alpha/beta. To this purpose a continuous-time version of Kallenberg's backward technique for computing Palm distributions of branching particle systems is developed, which permits us to adapt methods used by Dawson and Fleischmann in the study of discrete-space and discrete-time systems.