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2020-10-07,孙琪、李豆豆,分枝过程方向报告

报告一:

报告人:孙琪

单位:北京工商大学

时间:2020年10月7日 周三下午15:00-1600

线上腾讯会议,会议号:551638602

题目:Lower deviations for supercritical branching processes with immigration

摘要:

For a supercritical branching processes with immigration , it is known that under suitable conditions on the offspring and immigration distributions,  converges almost surely to a finite and strictly positive limit, where  is the offspring mean. We are interested in the limiting properties of  with  as . We give asymptotic behavior of such lower deviation probabilities in both Schr\"{o}der and B\"{o}ttcher cases, unifying and extending the previous results for non-immigration cases in literature.

This talk is based on joint work with Professor Mei Zhang.


报告二:

报告人:李豆豆

单位:北京工业大学

时间:2020年10月7日 周三下午16:00-1700

线上腾讯会议,会议号:551638602

题目:Harmonic moments and large deviations for a critical Galton-Watson process with immigration

摘要:

In this paper, a critical Galton-Watson branching process with immigration  is studied. We first obtain the convergence rate of the harmonic moment of . Then the large deviation of  is obtained, where  is a sequence of independent and identically distributed zero-mean random variables with tail index α>2. We shall see that the converging rate is determined by the immigration mean, the variance of reproducing and the tail index of , comparing to previous result for supercritical case, where the rate depends on the Schröder constant and the tail index.

This is a joint work with Professor Mei Zhang.