发布时间:2022-10-17
Strong and weak convergence rates of logarithmic transformed truncated EM methods for SDEs with positive solutions
主讲人:甘四清
摘要:To inherit numerically the positivity of stochastic differential equations (SDEs) with nonglobally Lipschitz coefficients, we devise a novel explicit method, called logarithmic transformed truncated Euler–Maruyama method. There is however a price to be paid for the preserving positivity, namely that the logarithmic transformation would cause the coefficients of the transformed SDEs growing super-linearly or even exponentially, which makes the strong and weak convergence analysis more complicated. Based on the exponential integrability, truncation techniques and some other arguments, we show that the strong convergence rate of the underlying numerical method is 1/2, and the weak convergence rate can be arbitrarily close to 1. To the best of our knowledge, this is the first result establishing the weak convergence rate of numerical methods for the general SDEs with positive solutions. Numerical experiments are finally reported to confirm our theoretical results
主讲人简介:甘四清,博士,中南大学教授,博士生导师,2001年毕业于中国科学院数学研究所,获理学博士学位,2001-2003年在清华大学计算机科学与技术系高性能计算研究所做博士后,曾先后访问美国、新加坡、香港等国内外名校。主要研究方向为确定性微分方程和随机微分方程数值解法。主持国家自然科学基金面上项目4项, 参加国家自然科学基金重大研究计划集成项目1项。在《SIAM J. Sci. Comput.》、 《BIT》、《Appl. Numer. Math.》、《J. Math. Anal. Appl.》、《中国科学》等国内外学术刊物上发表论文90余篇。2005年入选湖南省首批新世纪121人才工程。2014年湖南省优秀博士学位论文指导老师。
邀请人:黄乘明
时间:2022年10月20日(星期四)19:30-21:30
地点:腾讯会议室 ID:997254761