Stochastic generalized Kolmogorov systems with small diffusion: I. Explicit approximations for invariant probability density function
报告人：蒋达清
报告地点：腾讯会议ID: 190417737
报告时间：2024年11月26日星期二10:00-11:00
邀请人：刘群
报告摘要：
This paper presents long-term coexistence states of stochastic generalized Kolmogorov systems with small diffusion. Part I establishes a mathematical framework for approximating the invariant probability measures (IPMs) and density functions (IPDFs) of these systems. This paper introduces two new and easily implementable approximation methods, the log-normal approximation (LNA) and updated normal approximation (uNA), which can be used for systems with not only non-degenerate but also degenerate diffusion. Moreover, we utilize Kolmogorov-Fokker-Planck (KFP) operator and matrix algebra to develop algorithms for calculating the associated covariance matrix and verifying its positive definiteness. Our new approximation methods exhibit good accuracy in approximating the IPM and IPDF at both local and global levels, and significantly relaxes the minimal criteria for positive definiteness of the solution of the continuous-type Lyapunov equation. We demonstrate the utility of our methods in several application examples from biology and ecology.
主讲人简介：
蒋达清，男，理学博士，教授，博士生导师，主要从事随机微分方程方向的研究，研究由随机微分方程描述的生物各物种数量的变化规律， 预测种群和传染病最终的变化趋势（如灭绝性、持久性、不变分布、遍历性，周期性等），从而达到更好的维持生态平衡和防控传染病的目的。已发表300多篇SCI论文，主持高等学校全国优秀博士学位论文专项基金1项，主持4项国家自然科学基金面上项目。 获2008年全国百篇优秀博士论文、2010年获第五届“秦元勋数学奖”、汤森路透和科睿唯安2014-2020年全球高被引科学家、爱思唯尔2014--2023年中国高被引学者, 获2015年教育部自然科学奖二等奖。此外，他还是King Abdulaziz University兼职教授。
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