Strong convergence and asymptotic stability of explicit numerical schemes for nonlinear SDEs

主讲人：杨洪福  广西师范大学教师

时间：2021年11月5日14：00

地点：腾讯会议 516 157 788

举办单位：数理学院

主讲人介绍：杨洪福，博士，2019年毕业于东北师范大学，国防科技大学博士后，广西师范大学数学与统计学院教师。主要从事随机微分方程稳定性理论、应用及数值逼近的研究，在此研究方向上发表了学术论文近10篇，部分研究成果已发表在SIAM  J. Numer. Anal.、Math. Comp.、J. Differential Equations、Internat. J.  Control、Discrete Cont. Dyn.  Sys.-B、数学年刊A辑等；出版学术专著和研究生教材各1部；主持国家自然科学基金青年基金、广西省自然科学基金青年基金、广西科技计划人才专项项目各1项；参加国家自然科学基金面上项目1项。

内容介绍：In this article we introduce a number of explicit schemes, which are amenable to  Khasminski's technique and are particularly suitable for highly nonlinear  stochastic differential equations (SDEs). We show that without additional  restrictions to those which guarantee the exact solutions possess their  boundedness in expectation with respect to certain Lyapunov-type functions, the  numerical solutions converge strongly to the exact solutions in finite-time.  Moreover, based on the convergence theorem of nonnegative semimartingales,  positive results about the ability of the explicit numerical scheme proposed to  reproduce the well-known LaSalle-type theorem of SDEs are proved here, from  which we deduce the asymptotic stability of numerical solutions. Some examples  are discussed to demonstrate the validity of the new numerical schemes and  computer simulations are performed to support the theoretical results. This is a  joint work with Professors Xiaoyue Li and Xuerong Mao.