********************************************************************
Seminar
Department of Systems Engineering and Engineering Management
The Chinese University of Hong Kong
------------------------------------------------------------------------------------------
| Title | : | Almost Surely Exponential Stability of Numerical Methods for SDEs |
| Speaker | : | Prof. Xuerong Mao |
| University of Strathclyde, Glasgow | ||
| Date | : | March 23th, 2007 (Friday) |
| Time | : | 4:30 p.m. - 5:30 p.m. |
| Venue | : | Room 513 |
| William M.W. Mong Engineering Building | ||
| (Engineering Building Complex Phase 2) | ||
| CUHK | ||
------------------------------------------------------------------------------------------
Abstract:
| Most existing results are concerned with the mean square exponential stability of numerical methods for stochastic differential equations (SDEs) but few on the almost sure exponential stability which will be discussed in this paper. We shall show that that the trivial solution of a scalar linear SDE is almost surely exponentially stable if and only if the Euler-Maruyama (EM) method or the stochastic theta method applied to the SDE is almost surely exponentially stable for all sufficiently small step size. We then generalize our results to multi-dimensional nonlinear SDEs. We will show that when the SDE obeys the linear growth condition, the EM method recovers the almost surely exponential stability very well. We will also show that when the shift coefficient of the SDE obeys the one-side Lipschitz condition while the diffusion coefficient satisfies the linear growth condition, the backward Euler (BE) recovers the almost surely exponential stability very well. |
-------------------------------------------------------------------------------------------
Biography:
| Xuerong Mao reveived the Ph.D. degree on mathematics from Warwick University, England in 1989 and was then SERC (Science and Engineering Research Council, UK) Post-Doctoral Research Fellow 1989-92. Moving to Scotland, he joined the Department of Statistics and Modelling Science, University of Strathclyde, Glasgow as a lecturer in 1992, was promoted to Reader in 1995, and was made Professor in 1998 which post he still holds. He has authored 4 books and over 160 research papers. His main research interests lie in the field of stochastic analysis. He is a member of the editorial boards of several international journals including Journal of Stochastic Analysis and Applications and Journal of Dynamics of Continuous, Discrete & Impulsive Systems Series B. |
************************* ALL ARE WELCOME ************************
| Host | : | Prof. Xunyu Zhou |
| Tel | : | (852) 2609-8320 |
| : | xyzhou@se.cuhk.edu.hk | |
| Enquiries | : | Bolin Ding or Jeffrey Xu Yu |
| : | Department of Systems Engineering and Engineering Management | |
| CUHK | ||
| Website | : | http://www.se.cuhk.edu.hk/~seg5810 |
| : | seg5810@se.cuhk.edu.hk | |
********************************************************************