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【學術報告】2019年12月17日下午胡耀忠教授來我院舉辦學術講座

2019-12-16 15:57:56    瀏覽次數:

字體 色彩方案

報告人: 胡耀忠 教授(加拿大Alberta大學數學與統計科學系)

報告題目: Crank-Nicolson scheme for stochastic differential equations driven by fractional Brownian motions

報告摘要:We study the Crank-Nicolson scheme for stochastic differential equations (SDEs) driven by a multidimensional fractional Brownian motion $(B^{1},\dots, B^{m})$ with Hurst parameter $H>1/2$. It is well-known that for ordinary differential equations with proper conditions on the regularity of the coefficients, the Crank-Nicolson scheme achieves a convergence rate of $n^{-2} $, regardless of the dimension. In this paper we show that, due to   the interactions between the driving processes, $ B^{1},\dots, B^{m} $,   the corresponding Crank-Nicolson scheme for   $m$-dimensional  SDEs   has a slower   rate than for  one-dimensional  SDEs. Precisely, we shall prove that when the fBm is one-dimensional and  when the drift term is zero, the Crank-Nicolson scheme  achieves the    convergence rate $n^{-2H}$, and when   the drift term is non-zero, the exact rate turns out  to be $n^{-\frac12 -H}$. In the general multidimensional case the exact rate equals $n^{\frac12 -2H}$.  In all these cases the asymptotic error is proved to satisfy some linear SDE. We also consider the degenerated cases when the asymptotic error     equals   zero.

報告人簡介:胡耀忠,加拿大Alberta大學教授,1992年獲法國路易斯巴斯德大學概率博士學位,師從國際著名概率學家P.A.Meyer教授。長期從事隨機分析、金融數學的研究,在《Annals of Probability》、《Journal of Theoretical Probability》、《Stochastic Processes and their Applications》、《Probability Theory and Related Fields》以及《SIAM Journal of Control and Optimization》等國際頂尖雜志發表學術論文100余篇。2015年,由于他在隨機積分和隨機偏微分方程方面的重要工作,當選為Fellow of Institute of Mathematical Statistics。

報告時間: 2019年12月17日(星期二)下午16:00-18:00

報告地點: 科技樓南樓702室


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