報告人：王雄(約翰霍普金斯大學）

報告題目：Mean square stability of stochastic theta method for stochastic differential equations driven by fractional Brownian motion

報告摘要：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.

報告時間：2024年8月27日（星期二）16:00-18:00

報告地點：科技樓南樓706室

邀請人：黃乘明

報告人簡介：王雄，2022年博士畢業于阿爾伯塔大學（University of Alberta）, 目前在約翰霍普金斯大學（Johns Hopkins University）擔任J.J. Sylvester Assistant Professor。博士期間主要研究分數階高斯噪聲驅動的随機微分方程和偏微分方程（SDE/SPDE）以及解的長程行為。在高斯噪聲情形下，對于一系列随機偏微分方程的适定型問題和解的長程行為獲得一系列研究成果。目前的研究重心在随機環境中交互粒子系統的反問題。相關論文發表在 Ann. Inst. Henri Poincaré Probab. Stat.，Bernoulli， J. Differential Equations，J Comput Appl Math, Stoch. Partial Differ. Equ. Anal. Comput. 等主流數學期刊上。