Title:  Generalised Theory on Asymptotic Stability and Boundedness of

      Stochastic Functional Differential Equations

报告时间：7月8日16:30

报告地点：学院5号楼106教室

摘要

Abstract:  Asymptotic stability and boundedness have been two of most popular topics in the study of stochastic functional differential equations (SFDEs) . In general, the existing results on asymptotic stability and boundedness of SFDEs require (i) the coefficients of the SFDEs obey the local Lipschitz condition and the linear growth condition; (ii) the diffusion operator of the SFDEs acting on a $C^{2,1}$-function be bounded by a polynomial with the same order as the $C^{2,1}$-function.  However, there are many SFDEs which do not obey the linear growth condition. Moreover, for such highly nonlinear SFDEs, the diffusion operator  acting on a $C^{2,1}$-function is generally bounded by a polynomial with a higher order than the $C^{2,1}$-function.  Hence the existing criteria on stability and boundedness for SFDEs are not applicable and  we see the necessity to develop new  criteria.  Our main aim of this paper is to establish  new criteria where the linear growth condition is no longer needed while the up-bound for the diffusion operator may take a much more general form.

Introduction of Xuerong Mao

Xuerong Mao, professor, head of Department of Mathematics and Statistics, University of Strathclyde, UK. Professor Mao is a fellow of the Royal Society of Edinburgh and executive editor of Proceedings of the Royal Society of Edinburgh: Section A Mathematics. His research interests are stochastic systems, stochastic stability and attraction, approximate solutions , stochastic modelling in biochemical science and  stochastic neural networks