报告人：邵井海（天津大学应用数学中心）

报告时间：2026年1月3日（星期六）10:00-11:30

报告地点：科技楼南楼711室

报告摘要：The regime-switching processes are extensively used for modelling the realistic systems in control engineering, which experience abrupt changes in structure or parameters. This paper concerns the feedback stabilization problem of regime-switching processes with infinite environmental regimes based on the delayed discrete-time observations. We provide sharp criteria on the stability and instability of switching systems using the estimate of certain exponential functionals of continuous-time Markov chains and their skeleton Markov chains, which improves the existing results even the state space is finite. To overcome the difficulty caused by the switching processes in an infinite state space, we construct a new Markov chain on a finite state space to bound below pathwisely the switching processes on an infinite state space. Our method is applicable to state-independent and state-dependent regime-switching processes in an infinite state space.

报告人简介：邵井海，天津大学应用数学中心教授，博士生导师。2007年获得中国数学学会“钟家庆数学奖”，2008年, 获得“全国百篇优秀博士学位论文奖”。邵井海教授主要从事概率论遍历性理论、随机分析、随机微分方程方面的研究工作，多篇论文发表在著名数学刊物，包括J. Functional Analysis, Probability Theory and Related Fields, SIAM J. Control Optim, SIAM J. Math. Anal., Stochastic Processes and their Applications等。

邀请人：吴付科