讲座主题： An Introduction to Operator Fractional  Brownian Motions 

主讲人：肖益民

讲座时间：5月18日（周五）14:00-15:00

讲座地点：综合楼615会议室 

主讲人简介：美国密西根州立大学教授，主要从事随机场（包括高斯场，稳定随机场,无穷可分随机场）的分形几何、位势理论和连续时间随机游动方面的研究，取得了一系列具有国际先进水平的研究成果。  

2012年获聘为教育部长江讲座教授。多年连续主持美国国家自然科学基金多项，美国数理统计学会会士，SCI杂志《Statistics and  Probability Letters》共同主编，同时还是许多国际一流数学杂志的审稿人，如《Annals of  Probability》，《Annals of  Applied Probability》，《Transactions of  the AMS》, 《Probability Theory and Related Fields》, 《Journal of London  Mathematical Society》等。

摘要：Operator fractional Brownian  motions form a class of multivariate (or vector-valued) Gaussian processes with  stationary increments and operator-self-similarity. They arise naturally as  scaling limits of multivariate time series and have been studied rigorously in  probability theory and in statistics. Even though a lot of progress has been  made, there are still many open problems regarding their probabilistic  properties and statistical inferences. 

In this talk, I will provide an  introduction to operator fractional Brownian motions and discuss their basic  properties such as operator self-similarity, modulus of continuity, fractal  dimensions. I will also describe some recent work in the statistics literature  about the estimation problems for operator fractional Brownian motions.