Branching processes are mathematical models of the evolution of stochastic population systems. Measure-valued branching processes over abstract spaces were introduced by Watanabe (1968), who proved those processes arose as high-density limits of branching particle systems. The connection of the processes with stochastic evolution equations was first investigated by Dawson (1975). The study has been stimulated from different subjects including stochastic partial differential equations, nonlinear partial differential equations, random trees and graphs. The developments have also led to better understanding of results in those subjects thanks to the works of Aldous (1991, 1993), Dynkin (1994, 2002), Le Gall (1999) and many others. Based on our own work, this talk presents a brief review of the study focusing on its interplay with stochastic partial differential equations and nonlinear (quasi-linear) partial differential equations.
About the Speaker
Zenghu Li graduated from Beijing Normal University with his PhD degree in 1994. He is now holding a full professor position at this University. He has published more than 80 research papers on measure-valued branching Markov processes, stochastic differential equations and related topics. His book “Measure-valued branching Markov processes” was published by Springer in 2011. He is now the president of the Chinese Association of Probability and Statistics and the associate editor of a number of mathematical journals including Acta Mathematica Sinica and Stochastic Processes and Their Applications. He was elected as a Fellow of the Institute of Mathematical Statistics in 2012.