报告内容: Stability characterisation of stochastic Volterra equations with applications to financial markets
报告人姓名: John Appleby
报告人所在单位: Dublin City University,Ireland
报告时间: 2018年7月6日 周五下午3:30
报告人简介: John Appleby is a Professor of Mathematics in the School of Mathematical Sciences, Dublin City University (DCU), Ireland. He received his PhD in Applied Mathematics from DCU 1999, and was promoted to Professor in 2013. He has published more than 100 papers in stochastic and deterministic dynamical systems. His research interests lie the asymptotic analysis of these systems, in particular those which are highly nonlinear, or possess memory. He has given around 100 talks at conferences and university colloquia worldwide. He has supervised successfully 11 PhD students and been awarded over €1m in external funding support for his research. He is an associate editor of the Electronic Journal of the Qualitative Theory of Differential Equations and acts as a reviewer for many of the main journals in differential equations and stochastic analysis.
报告摘要：The talk is concerned with characterising the asymptotic behaviour of solutions of linear and affine stochastic functional differential equations. In each case, there is an equilibrium state at zero when the equation is not perturbed by noise. Mainly we study Volterra equations, but we also study functional differential equations with finite delay.
In the affine case, the drift is autonomous and the diffusion coefficient is independent of the state. The results give necessary and sufficient conditions (in terms of the underlying deterministic differential resolvent and the decay of the norm of the diffusion matrix), for solutions to tend to a steady state, be bounded or be unbounded, almost surely.
In the linear case, we give very sharp sufficient conditions for the solution to be stable in a mean square sense. In the scalar case, these results are necessary and sufficient for mean square stability. These scalar results are then applied to establish the presence of stationary and highly correlated volatility in an microeconomic model of a financial market.
The results presented are in part joint with Xuerong Mao (Strathclyde, Glasgow) and Markus Riedle (King's College London).
报告内容: Stochastic differential equations driven by Levy processes
报告时间: 2018年7月6日 周五下午5:00
报告人简介: 陈振庆，美国华盛顿大学（西雅图）数学系教授、国家“千人计划”特聘专家、“长江学者奖励计划”讲座教授。陈振庆教授是国际顶级期刊《The Annals of Probability》的副主编，国际顶级期刊《Potential Analysis》和《Proceedings of the American Mathematical Society》的主编，《中国科学》等众多期刊的编委。陈振庆教授1992年在美国华盛顿大学（圣路易斯）获博士学位，曾在美国的加利福尼亚大学（圣地亚哥）和康奈尔大学工作；1998年起在位于华盛顿州西雅图市的华盛顿大学数学系工作至今。主要从事概率论及随机过程的研究，主要研究方向是：随机分析，随机微分方程，马氏过程及其位势理论，狄氏型，发表论文150余篇。