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

报告时间：2017年10月23日下午16:00

报告地点：知新楼B座1238

Abstract： A continuous-state branching processes in random environment (CBRE-process) is defined as the strong solution of a stochastic integral equation. The environment is determined by a Levy process with no jump less than -1. Characterizations of the quenched and annealed transition semigroups of the process can be given in terms of a backward stochastic integral equation. The process hits zero with strictly positive probability if and only if its branching mechanism satisfies| Grey's condition. In that case, a characterization of the extinction probability is given using a random differential equation with singular terminal condition. The strong Feller property of the CBRE-process can be established by a coupling method. A criterion for the ergodicity of a subcricital CBRE-process with immigration can be given by an integral condition. This is a brief survey of the recent progresses in the subject.

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