Small value probabilities for continuous state branching processes with immigration  

作　　者：CHU WeiJuan LI WenBo V REN YanXia 

机构地区：[1]Department of Mathematics, Nanjing University, Nanjing 210093, China [2]Department of Mathematical Sciences, University of Delaware, Newark, DE 19716, USA [3]LMAM, Center for Statistical Science, School of Mathematical Sciences, Peking University, Beijing 100871, China

出　　处：《Science China Mathematics》2012年第11期2259-2271,共13页中国科学：数学（英文版）

基　　金：supported by National Science Foundation of US (Grant Nos. DMS-0805929 and DMS-1106938);National Natural Science Foundation of China (Grant Nos. 10928103,10971003 and 11128101);Specialized Research Fund for the Doctoral Program of Higher Education of China;the Fundamental Research Funds for the Central Universities

摘　　要：We consider the small value probability of supercritical continuous state branching processes with immigration. From Pinsky （1972） it is known that under regularity condition on the branching mechanism and immigration mechanism, the normalized population size converges to a non-degenerate finite and positive limit PV as t tends to infinity. We provide sharp estimate on asymptotic behavior of P（W≤ε〈） as ε→ 0＋ by studying the Laplace transform of W. Without immigration, we also give a simpler proof for the small value probability in the non-subordinator case via the prolific backbone decomposition.We consider the small value probability of supercritical continuous state branching processes with immigration.From Pinsky(1972) it is known that under regularity condition on the branching mechanism and immigration mechanism,the normalized population size converges to a non-degenerate finite and positive limit W as t tends to infinity.We provide sharp estimate on asymptotic behavior of P(W≤ε) as ε→ 0+ by studying the Laplace transform of W.Without immigration,we also give a simpler proof for the small value probability in the non-subordinator case via the prolific backbone decomposition.

关 键 词：continuous state branching process small value probability IMMIGRATION 

分 类 号：O211.65[理学—概率论与数理统计] O213.2[理学—数学]