报告题目:Fully discrete schemes and Lp-strong convergence orders for the SPDE driven by Levy noise

报告人: 雷子伊

报告日期：6月27日 星期六

报告时间：15：30-16：00

报告地点：逸夫楼1537

报告摘要：Stochastic partial differential equations (SPDEs) driven by Levy noise naturally arise in physical systems exhibiting abrupt or discontinuous random effects, whose temporal Holder continuity in Lp sense is known to be at most 1/p resulting from the Burkholder-Davis-Gundy inequality. This poses a challenge in the numerical analysis for achieving the uniform Lp-strong convergence orders of numerical schemes for p ≥ 2. In this paper, we develop a discretization framework for constructing fully discrete schemes tailored to different conditions of Levy measures, whose spatial direction is based on the spectral Galerkin method and temporal direction employs the Euler-type method. For the case of finite Levy measures, a jump-adapted time discretization is utilized for the equation that may involve multiplicative noise; while for infinite Levy measures, we introduce an approach based on the quantitative John-Nirenberg inequality for SPDEs driven by additive Levy noise. We prove that proposed schemes converge in Lp sense with orders almost 1/2 in both space and time for all p ≥ 2, which contributes novel results in the numerical analysis of the SPDE driven by Levy noise.