时间：2021年3月2日

地点：数理楼一楼小报告厅 145 (上午线下报告：8:30-11:30）

腾讯会议：212 244 431 （下午线上报告：15:00-17:00）

欢迎大家参加！ (本研讨会相关费用由学院教师个人科研经费支持)

报告题目1: Criterion for the existence of a quasi-stationary distribution for birth-death processes with killing

报告人: 张汉君, 湘潭大学

时间：8:30-9:30

报告人简介：张汉君，教授，博士生导师。1988年7月获博士学位，1995年7月破格晋升为教授，1999年由铁道部专家组授予博士生导师资格。2001年至2007年在著名的澳大利亚Queensland大学担任中心研究员，曾多次到英国、德国、加拿大、法国、香港、智利等国家和地区的著名学府进行合作研究与学术交流；现为湘潭大学教授，主要从事拟平稳分布理论研究工作。在国内外核心刊物上发表论文60余篇，先后获得国家教育委员会科学技术进步二等奖、全国优秀科技图书二等奖、湖南省科学技术进步一等奖、湖南省教育委员会科技进步一等奖、铁道部“中青年有突出贡献专家”、澳大利亚ARC Centre Fellow。

报告摘要: In this talk, we consider birth-death processes on the nonnegative integers, where C={1,2,…} is an irreducible class, 0 is absorbing state, with the additional feature that a transition to state 0 (killing) may occur from any state. Assuming that absorption at 0 is certain, we obtain the additional conditions on transition rates for the existence of a quasi-stationary distribution.

报告题目2: Invariant probability measures for McKean-Vlasov SDEs with memory

报告人: 鲍建海, 天津大学

时间：9:30-10:30

报告人简介：鲍建海，天津大学应用数学中心研究员，主要研究方向为随机分析。目前先后在Stoch. Proc. Appl.，Bernoulli, Electron. J. Probab., SIAM J. Control Optim., SIAM J. Math. Appl.，JDE, Potential Anal., IME等期刊上发表多篇学术论文。

报告摘要: In this talk, we first overview some existing approaches to show existence of invariant probability measures for linear Markov processes. Then we put forward an approach to show existence of invariant probability measures for McKean-Vlasov stochastic differential equations with memory, which are typical nonlinear Markov processes. With contrast to the classical SDEs, we derive similar sufficient conditions to guarantee existence of invariant probability measures for McKean-Vlasov SDEs.

报告题目3: Quasi-stationary behavior for Markov-modulated Markov chains

报告人: 李文迪，中南大学

时间：10:30-11:30

报告人简介：李文迪，中南大学博士生，主要研究方向为马氏过程、应用概率等。目前在《Advances in Applied Probability》，《 Journal of Applied Probability》，《Queueing Systems》， 《Operation Research Letters》上发表4篇学术论文。

报告摘要: In this talk, we present the quasi-stationary distribution for Markov-modulated Markov chains. We focus on two fundamental aspects (existence and uniqueness, domain of attraction) in connection with quasi-stationary distribution.  We first provide a sufficient criterion for the existence of the quasi-stationary distribution.  An iterative algorithm to compute all quasi-stationary distributions is presented. We then carry out a study on the domain of attraction for the quasi-stationary distribution under a uniqueness condition.  In addition, we apply the results to M/G/1-type Markov chains, and characterize the asymptotic behavior of the quasi-stationary distribution for this model. Finally, a scalar example is given to illustrate these results.

报告题目4: Deviation properties for quadratic functionals of linear self-interacting diffusion process and applications

报告人: 蒋辉，南京航空航天大学

时间：15:00-17:00

报告人简介：蒋辉，教授，博士生导师。主要从事随机分析、大偏差、随机过程的统计推断等研究，在Stochastic Processes and their Applications, Annals of Statistics, Journal of Applied Probability, Journal of Theoretical Probability等期刊发表论文四十余篇。主持国家自然科学基金3项，中国博士后基金2项。

报告摘要: In this talk, we study the deviation properties, including the deviation inequalities and Cram\'{e}r-type moderate deviations, for some quadratic functionals of linear self-interacting diffusion process. Our results contain both self-repelling and self-attracting cases. As applications, Cram\'{e}r-type moderate deviations for the log-likelihood ratio process and drift parameter estimator are obtained. The main methods consists of the deviation inequalities for multiple Wiener-It\^{o} integrals, as well as the asymptotic analysis techniques.  This is a joint work with Yajuan PAN.