报告 人：李增沪教授 (北京师范大学)
报告题目：Continuous-state branching processes in Levy environments
A continuous-state branching processes inrandom environment (CBRE-process) is defined as the strong solution of astochastic integral equation. The environment is determined by a Levy processwith no jump less than -1. Characterizations of the quenched and annealedtransition semigroups of the process can be given in terms of a backwardstochastic integral equation. The process hits zero with strictly positiveprobability if and only if its branching mechanism satisfies| Grey's condition.In that case, a characterization of the extinction probability is given using arandom differential equation with singular terminal condition. The strongFeller property of the CBRE-process can be established by a coupling method. Acriterion for the ergodicity of a subcricital CBRE-process with immigration canbe given by an integral condition. This is a brief survey of the recentprogresses in the subject.