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


主講人:甘四清 中南大學教授 博士生導師




主講人介紹:中南大學二級教授、博士生導師。2001年畢業于中國科學院數學研究所獲理學博士學位,2001-2003年在清華大學計算機科學與技術系高性能計算研究所做博士后。主要研究方向為確定性微分方程和隨機微分方程數值解法。主持國家自然科學基金面上項目3項,  參加國家自然科學基金重大研究計劃集成項目1項。在《SIAM Journal on Scientific Computing》、 《BIT Numerical  Analysis》、《Journal of Mathematics Analysis and  Applications》、《中國科學》等國內外學術刊物上發表論文80余篇。2005年入選湖南省首批新世紀121人才工程。2014年湖南省優秀博士學位論文指導老師。

內容介紹: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.