Some Limit Theorems for a Particle System of Single Point Catalytic Branching Random Walks

作     者：Vladimir VATUTIN Jie XIONG 

作者机构：Steklov Mathematical Institute Gubkin street 8 119991 Moscow Russia Department of Mathematics University of Tennessee Knoxville TN 37996 1300 USA Department of Mathematics Hebei Normal University Shijiazhuang 050016 P. R. China 

出 版 物：《Acta Mathematica Sinica,English Series》 (数学学报（英文版）)

年 卷 期：2007年第23卷第6期

页      面：997-1012页

核心收录：

学科分类：02[经济学] 0202[经济学-应用经济学] 020208[经济学-统计学] 07[理学] 0714[理学-统计学（可授理学、经济学学位）] 070103[理学-概率论与数理统计] 0701[理学-数学] 

基　　金：DFG grants RFBR 02-01-00266 Russian Scientific School 1758.2003.1 NSA Alexander von Humboldt Foundation 

主　　题：Renewal equation branching particle system scaling limit 

摘      要：We study the scaling limit for a catalytic branching particle system whose particles perform random walks on Z and can branch at 0 only. Varying the initial （finite） number of particles, we get for this system different limiting distributions. To be more specific, suppose that initially there are n^β particles and consider the scaled process Zt^n（·） = Znt（√n·）, where Zt is the measure-valued process 1 and to a representing the original particle system. We prove that Ztn converges to 0 when β 〈1/4 and to a nondegenerate discrete distribution when β=1/*** addition,if 1/4〈β〈1/2 then n-^（2β-1/2）Zt^n converges to a random limit,while if β 〉21then n^-βZtn converges to a deterministic limit.