报告人：王雄(约翰霍普金斯大学）

报告题目：Mean square stability of stochastic theta method for stochastic differential equations driven by fractional Brownian motion

报告摘要：In this work, we study the mean square stability of the solution and its stochastic theta scheme for the following stochastic differential equations driven by fractional Brownian motion with Hurst parameter H∈(1/2,1): dX(t)=f(t,X(t))dt+g(t,X(t))dB^H (t). Firstly, we consider the special case when f(t,X)=-λκt^(κ-1) X and g(t,X)=μX. Secondly, the stability of the solution and its stochastic theta scheme for nonlinear equations is studied. Due to presence of long memory, even the problem of stability in the mean square sense of the solution has not been well studied, let alone the stability of numerical schemes. A complete new set of techniques to deal with this difficulty are developed. Numerical examples are carried out to illustrate our theoretical results.

报告时间：2024年8月27日（星期二）16:00-18:00

报告地点：科技楼南楼706室

邀请人：黄乘明

报告人简介：王雄，2022年博士毕业于阿尔伯塔大学（University of Alberta）, 目前在约翰霍普金斯大学（Johns Hopkins University）担任J.J. Sylvester Assistant Professor。博士期间主要研究分数阶高斯噪声驱动的随机微分方程和偏微分方程（SDE/SPDE）以及解的长程行为。在高斯噪声情形下，对于一系列随机偏微分方程的适定型问题和解的长程行为获得一系列研究成果。目前的研究重心在随机环境中交互粒子系统的反问题。相关论文发表在 Ann. Inst. Henri Poincaré Probab. Stat.，Bernoulli， J. Differential Equations，J Comput Appl Math, Stoch. Partial Differ. Equ. Anal. Comput. 等主流数学期刊上。