Moments and large deviations for multitype branching processes in random environments
数学学科创建110周年系列报告
报告题目(Title)：Moments and large deviations for multitype branching processes in random environments
报告人(Speaker)：Quansheng Liu（Univ. Bretagne Sud, France）
地点(Place)：后主楼1220
时间(Time)：2025年5月23日（周五）10:00-11:00
邀请人(Inviter)：高志强
报告摘要
Consider a $d$-type supercritical branching process $Z_n$ $ =(Z_n(1), \cdots$, $ Z_n(d)), $ $ \,n\geq 0,$ in an independent and identically distributed random environment $\xi =(\xi_0, \xi_1, \ldots)$, % starting with one initial particle of type $i$, whose offspring distributions of generation $n$ depend on the environment $\xi_n$ at time $n$. We present a precise asymptotic of the moments and a Bahadur-Rao type large deviation expansion for the total population size $\| Z_n \|_1 = \sum_{j=1}^d Z_n(j) $ of generation $n$. In the approach, we use Cram\'er type measure change, and establish under the changed measure,
a Perron-Frobenius type theorem and the stable convergence for products of random positive matrices, and $L^p$ convergence for the multi-type branching process. (Joint work with Ion Grama and Thi Trang NGUYEN)
主讲人简介
刘全升教授是法国南布列塔尼大学的特级教授，博士生导师。曾任大西洋布列塔尼数学实验室的副主任和南布列塔尼大学数学实验室主任。他的研究领域广泛，在多个领域均有建树，如在概率统计、分形几何和数字图像处理等领域，特别是在对大偏差理论、随机矩阵乘积、分枝过程、分枝随机游动和图像去噪等方面都有出色的研究成果。他与合作者在《J. Eur. Math. Soc.》、《Probab. Th. Rel. Fields》、《Annals of Probability》、《Annals of Applied Probability》、《Bernoulli》、《Stochastic Processes and Applications》和《Annals of Inst. Henri Poincaré》等国际顶级期刊上发表了多篇论文，曾多次受邀到国内外著名大学进行交流访问，多次在重要国际会议上做邀请报告。
