报告人: 谢南瑞（台湾大学）

时  间: 2018年10月16日  下午16:00-17:00

        2018年10月17日  上午10:00-11:00

地  点: 理科楼 LD202

摘  要: We begin with the mathematical definition and the stochastic properties of Brownian Motions (BMs) in $\R^d, d\ge 1$. Then, we discuss two BM path properties; one is common for all $d$, and one is sharply different for different $d=1,2,3$. Then, we discuss  four random sets defined by a BM path and their fractal dimensions.  The goal is to attract the attention to the planar BM paths, of which completely new fractal dimensions results, among others,  lead two Fields Medals 2006 and 2010.

The references:

G.F. Lawler: Conformally Invariant Processes in the Plane. AMS 2012.

P. Morters and Y. Peres: Brownian Motion. CUP 2010.

P. Morters:  Sample path properties of BM. Berlin Math School LNs, 2011.

K. Falconer: Textbooks on Fractal Geometry.

N.-R. Shieh: several published papers related to sample-paths properties.

报告人简介: 谢南瑞，台湾大学数学系名誉教授，国际知名概率论专家。研究兴趣有：Probability, Stochastic Processes, and Stochastic Analysis, with aspects on (multi) scaling and fractality in random structures, random function analysis, Wiener’s chaos expansions, spatial-temporal random fields, exponential processes, wavelets in stochastics, applications in mathematical analysis and in financial economics .目前已发表学术论文七十篇。

学院联系人:罗 军

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