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学术报告:Kesten-Stigum theorem for a branching process in a random environment and Perron-Frobenius theorem for products of positive random matrices
2025/06/06 10:52:31     ( 点击:)

报告摘要:LetZn=(Zn(1), ...,Zn(d)) be a supercriticald-type branching process in an independent and identically distributed random environmentξ= (ξ0,ξ1, ....). Given the environment, all particles behave independently, and eachr-type particle of generationngives birth to new particles of the next generation of types 1, ... ,daccording to a probability distributionpr(ξn) =prk(ξn): k∈Ndon Nd, depending onξnandr, for eachr∈{1, ...,d}. We establish a Kesten-Stigum type theorem, which gives a precise description of the growth rate of the population size, and which builds a bridge between the branching process and products of nonnegative random matrices. For the proof, we establish a Perron-Frobenius type theorem for products of stationary and ergodic nonnegative random matrices, which gives a precise description of the size of such products, and which offers a close link with the ergodic theory for stationary and ergodic sequences of real random variables. (Based on joint works with Ion Grama, Thi Trang Nguyen and Erwan Pin)

个人简介:刘全升,法国特级教授,就职于南布列塔尼大学,享受法国优秀科研津贴(PES/PEDR)。1984年获得武汉大学数学系本科文凭,1993年获得巴黎六大概率论专业博士文凭 。1993至2000年任法国雷恩大学讲师 、副教授。2000年9月起任法国南布列塔尼大学教授。长期担任南布列塔尼大学数学实验室主任(Directeur du Laboratoire de Mathématiques) ;主导创建了应用数学第三阶段文凭(DESS)、数学和应用数学硕士文凭(Master),并长期负责数学与应用数学专业研究生培养工作。

研究课题涉及概率统计,分形几何和数字图像处理。近年主要研究随机环境中的概率统计问题,尤其是关于大偏差理论、随机矩阵乘积,几类重要的随机环境的数学物理和应用概率模型,包括分枝过程、分枝随机游动和图像去噪等。在《J. Eur. Math. Soc.》、《Annals of Probability》、《Probab. Th. Rel. Fields》、《Annals of Applied Probability》、《IEEE Trans. Image Processing》等期刊上发表论文100余篇。

报告时间:2025年6月7日8:30 -11:30

报告地点:北衡楼1420

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