主讲人简介：任艳霞教授是北京大学数学学院教授、博士生导师、中国概率统计学会常务理事、全国百篇优秀博士论文获得者。

内容摘要：Consider any supercritical Galton-Watson process which may become extinct with positive probability. It is a well-understood and intuitively obvious phenomenon that, on the survival set, the process may be pathwise decomposed into a stochastically `thinner' Galton-Watson process, which almost surely survives and which is decorated with immigrants, at every time step, initiating independent copies of the original Galton-Watson process conditioned to become extinct. The thinner process is known as the backbone and characterizes the genealogical lines of descent of prolific individuals in the original process. Here, prolific means individuals who have at least one descendant in every subsequent generation to their own.

Starting with Evans and O'Connell (1994), there exists a cluster of literature describing the analogue of this decomposition for a variety of different classes of superprocesses and continuous-state branching processes.

I will talk our results concerning backbone decompositions and describe a result for a general class of supercritical superprocesses with spatially dependent branching mechanisms.

讲座语言：汉语