Mean-square approximations of jump-diffusion SDEs with super-linearly growing diffusion and jump coe


主讲人:甘四清 中南大学教授 博士生导师




主讲人介绍: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。

内容介绍:In this talk, we first establish 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.