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 immigrati...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.展开更多
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)+1 种基金Specialized Research Fund for the Doctoral Program of Higher Education of Chinathe Fundamental Research Funds for the Central Universities
文摘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.
