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报告题目：Large deviations principles of sample paths and invariant measures of numerical methods for parabolic SPDEs

报告人：  陈子恒  副教授

报告人简介： 2019年博士毕业于中南大学，获计算数学专业博士学位；2019年至2021年在中科院数学院从事博士后研究工作；目前研究方向为随机微分方程数值解法，主要分析数值方法的收敛性、遍历性和大偏差理论等。现就职于云南大学数学与统计学院。

摘要：For parabolic stochastic partial differential equations (SPDEs), we show that the numerical methods, including the spatial spectral Galerkin method and further the full discretization via the temporal accelerated exponential Euler method, satisfy the uniform sample path large deviations. Combining the exponential tail estimate of invariant measures, we establish the large deviations principles (LDPs) of invariant measures of these numerical methods. Based on the error estimate between the rate function of the considered numerical methods and that of the original equation, we prove that these numerical methods can weakly asymptotically preserve the LDPs of sample paths and invariant measures of the original equation. This work provides an approach to proving the weakly asymptotical preservation for the above two LDPs for SPDEs with small noise via numerical methods, by means of the minimization sequences.

时间：2021年10月28日（周四）下午3:00-5:00

腾讯会议号：833 369 360

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