An approximation of a class of functional differential equations with wideband noise perturbations
报 告 人:: 吴付科
报告地点:: 数学与统计学院617报告厅
报告时间:: 2018年07月14日星期六10:10-10:50

   In contrast to the use of white noise in stochastic models, wideband noise is more realistic for various applications. White noise is a good process to work with, but it is difficult to realize in real applications, whereas wideband noise is a good approximation to white noise. This work is focused on functional differential equations subject to wideband noise. By virtue of the ideas of functional derivatives developed in recent work on functional It\^o formula, using perturbed test function methods combined with martingale techniques, this paper shows that when the small parameter tends to zero, the underlying process converges to a limit that is governed by solutions of a stochastic functional differential equation. This paper also gives an integro-differential system with wideband noise as an example and examines its asymptotic properties. Not only are the results interesting from a mathematical point of view, but also they will be of great utility to a wide range of problems in control and optimization problems.

发 布 人:吴双 发布时间: 2018-07-11
吴付科教授,1976年11月生于河南邓州,2003年博士毕业于华中科技大学数学与统计学院。主要从事随机微分方程以及相关领域的研究,2011年入选教育部新世纪优秀人才支持计划,2012年入选华中科技大学“华中学者”,2014年获得基金委优秀青年基金资助。近年来,在SIAM J. Appl. Math., SIAM J. Numer. Anal., SIAM J. Control Optim., Numer. Math., J. Differential Equations, Automatica和IEEE TAC等国际权威期刊发表论文70余篇,全部为SCI收录。共主持3项国家自然科学基金和一项教育部新世纪优秀人才基金,出版一部专著 (与胡适耕教授和黄乘明教授合著:随机微分方程,科学出版社, 2008) 和一部译著 (与刘金山副教授合译:随机微分方程:导论与应用, 科学出版社, 2012年). 先后应邀访问英国、德国、美国、澳大利亚等国家的学术机构.