报告人:甘四清（中南大学）

报告人简介: 甘四清, 中南大学二级教授、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。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3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 Journal on Scientific Computing》、 《BIT Numerical Analysis》、《Journal of Mathematics Analysis and Applications》、《中国科学》等国内外学术刊物上发表论文80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。

报告题目：Mean-square approximations of jump-diffusion SDEs with Super-linearly growing diffusion and jump coefficients

报告摘要：This paper first establishes a fundamental mean-square convergence theorem for general one-step numerical approximations of stochastic differential equations (SDEs) driven by Wiener process and compound Poisson process, with non-globally Lipschitz coefficients. Then two novel explicit schemes are designed and their convergence rates are exactly identified via the fundamental theorem. Different from existing works, we do not impose a globally Lipschitz condition on the jump coefficient but formulate appropriate assumptions to allow for its super-linear growth. Moreover, new arguments are developed to handle essential difficulties in the convergence analysis, caused by the super-linear growth of the jump coefficient and the fact that higher moment bounds of the Poisson increments $\int_t^{t+h}\int_Z\bar{N}(ds; dz); t\geq 0, h > 0$ contribute to magnitude not more than O(h). Numerical results are finally reported to confirm the theoretical findings.

报告时间：2019年5月9日 20：30 

报告地点：科技楼南楼702室