报 告 人：马春生教授
报告题目：Brownian motion and its applications
报告时间：2015年6月17日（周三）上午10:00
报告地点：静远楼1508学术报告厅
Abstract: This talk is mainly about the history of Brownian motion. The physical phenomenon of Brownian motion is usually attributed to R. Brown (1828) and was explained by A. Einstein (1905), whose explanation of the phenomenon was a milestone in the establishment of the atomistic world view of physics. The first study of the mathematical process of Brownian motion is due to L. Bachelier (1900) in the context of modeling stock market flucunations, but his work was long forgotten and has only recently been rediscovered: today an international society for mathematical finance is named after him. The first rigorous construction of mathematical Brownian motion is due to N. Wiener (1923), and in his honor Brownian motion is sometimes called the Wiener process. A lot of effort in the literature has been put into trying to extend the understanding of Brownian motion to more general Gaussian processes, such as the fractional Brownian motion that was introduced by A. N. Kolmogorov (1940) and named by B. B.Mandelbrot and J. W. Van Ness (1968). In this talk we introduce three types ofcovariance matrix structures for Gaussian or elliptically contoured vector random fields in space and/or time, which include fractional, bifractional, and trifractional vector Brownian motions as special cases, and reveal the relationships among these vector random fields, with an orthogonal decomposition established for the multifractional vector Brownian motion.
马春生教授个人简介：
马春生1997年博士毕业于澳大利亚悉尼大学太阳成集团，之后到加拿大英属哥伦比亚大学统计系作博士后。1999年起在美国威启达州立大学数学与统计学系工作，现为该校终身教授，博士生导师。2006年至2007年为美国北卡罗拉州统计与应用数学科学学院的研究员。2009年至2010年被聘为武汉大学的客座教授。2011年起为武汉理工大学经济学院的特聘教授、楚天学者.2013年起为湖北工程学院的客座教授.马教授的主要科研方向为概率论、数理统计及其应用，已发表70篇学术论文（75%为单一作者）于30多种国内外学术杂志上.他的研究课题获得了美国国家自然科学基金、美国能源部、堪萨斯州、及其它科研基金的资助，为30多种国际学术杂志（包括概率、统计、计量经济、精算学、信息论、信号处理、系统科学、环境科学、数理空间科学等方面）的审稿人，还为美国国家自然科学资金评审过课题申请报告，现为两概率统计杂志的编委。