报告题目：Spinedecompositions and limit results for models with branching structure

报 告 人：任艳霞教授, 北京大学数学科学学院

报告时间：2018年8月8日下午16:00-17:00

报告地点：苏州大学金融工程研究中心105学术报告厅

Abstract: Consider a Galton-Watson process with offspring distribution. Let be a random variable with law.Assume that and the process is critical in the sense that

                            (1)

Suppose has finite variance

                            (2)

Forsimplicity, we will call a Galton-Watson process with offspring distribution a μ-Galton-Watson process.

In thistalk, I will describe a 1-spine decomposition and a 2-spine decomposition forthe critical Galton-Watson tree and use the 2-spine decomposition to give aprobabilistic proof of Yaglom’s theorem: conditional on, thelaw of converges to the exponential distribution.

Then Iwill establish a 1-spine decomposition theorem and a 2-spine decompositiontheorem for some critical superprocesses. These two kinds of decompositions areunified as a decomposition theorem for size-biased Poisson random measures.These decompositions to can be used to give probabilistic proofs of theasymptotic behavior of the survival probability and Yaglom’s exponential limitlaw for some critical superprocesses.

Thetalk is based on a joint works with Renming Song and Zhenyao Sun.

任艳霞教授简介：1998年在南开大学取得博士学位，之后在清华大学高等研究中心做博士后两年。2000年开始在北京大学任教，2003年被聘为教授。研究领域为测度值马氏过程、分支粒子系统等，发表论文五十多篇。2000年获全国优秀博士论文奖，连续多年获得国家自然科研基金资助。曾到加拿大多伦多大学、英属哥伦比亚大学及美国伊利诺伊大学、俄勒冈大学、华盛顿大学等进行学术访问。现任博士生导师、概率统计系主任、中国概率统计学会常务理事。