报告题目1：A frequency domain for the stabilizing feedback controller of linear delay systems
报告人：胡广大
报告时间：2022年11月26日 13:30
报告地点：腾讯会议 ID 742-454-293
主办单位：安徽省高端装备智能控制国际联合研究中心，高端装备先进感知与智能控制教育部重点实验室，数理与金融学院，科技处，研究生部
报告人简介：胡广大, 上海大学数学系教授，博导，运筹学与控制论研究所所长。1996获得日本国名古屋大学计算机科学系博士， 1999-2000年加拿大纽芬兰大学计算机科学系博士后。曾访问英国曼彻斯特大学，加拿大约克大学。先后任教于哈尔滨工业大学和北京科技大学。2011年以来至今，任国际SCI杂志“Journal of Computational and Applied Mathematics”编委。主要研究方向是控制系统设计的数值最优化方法和.微分方程的数值分析。研究成果分别被意大利和美国学者的专著收录为定理。于2006年获得黑龙江省科技进步一等奖（自然科学类）以及全球前2%顶尖科学家榜单。主持国家自然科学基金5项和教育部博士点基金1项。在IEEE Trans. Automatic Control, IEEE Trans. Signal Processing, International Journal of Control，BIT Numeral Mathematics，J. Comput. Appl. Math.，等国际SCI杂志上发表论文70多篇。由Springer出版英文教材一部。
报告摘要：We investigate feedback stabilization of linear delay systems. When the unstable characteristic roots of the system are far from the imaginary axis, the discretization of unstable differential equations results in a large error. In this case, it is difficult to seek stabilizing control laws via the algorithm in the literature. In order to avoid the discretization of unstable differential equations, a modified state equation is constructed through a shifting parameter such that the equation is asymptotically stable. Then, based on the modified state equation and Parseval’s theorem, a numerical optimization algorithm is provided to design a stabilizing controller. Meanwhile, we compare the presented algorithm with that in the literature. Finally, numerical examples are given to illustrate the presented algorithm.
报告题目2：Compensated split-step balanced methods for nonlinear stiff SDEs with jump-diffusion and piecewise continuous arguments
报告人：张诚坚
报告时间：2022年11月26日 14:00
报告地点：腾讯会议 ID 742-454-293
主办单位：安徽省高端装备智能控制国际联合研究中心，高端装备先进感知与智能控制教育部重点实验室，数理与金融学院，科技处，研究生部
报告人简介：张诚坚, 华中科技大学二级教授, 博士生导师. 1998年毕业于湖南大学应用数学专业获理学博士学位后, 调入华中理工大学数学系，并同时进入该校控制科学与工程博士后流动站工作(2000年出站). 2002年2月至2004年3月在比利时鲁汶大学计算机科学系做合作研究工作.曾担任华中科技大学数学与统计学院院长、中国数学学会第十届、十一届理事、中国计算数学学会第七届、八届常务理事及湖北省数学学会副理事长. 现兼任中国仿真算法专业委员会副主任委员、中国数学学会奇异摄动专业委员会委员、湖北省工程建模与科学计算重点实验室主任、《Applied Mathematics and Computation》副主编及《Mathematics and Computers in Simulation》、《Acta Mathematica Scientia》等国际学术期刊编委.主要从事刚性时滯微分方程数值解及其算法理论研究，主持有国家自然科学基金面上项目6项、教育部留学回国人员启动基金及湖北省自然科学基金各1项，并作为主要成员承担过国家自然科学基金重大研究计划课题和国家高技术研究发展计划重点项目. 在《SIAM J. Sci. Comput.》、《IMA J. Numer. Anal. 》、《Numer. Math.》等国内外学术期刊发表SCI收录论文100余篇，主、参编教材5部，主持有国家级精品课程及国家级精品资源共享课《计算方法》. 曾获国务院政府特殊津贴、机械工业部科技进步二等奖、湖北省自然科学奖二等奖、湖北省有突出贡献的中青年专家、宝钢优秀教师奖、湖北省优秀教学成果一等奖及湖北省优秀教育工作者等.
报告摘要：This talk is concerned with numerical solutions of nonlinear stiff stochastic differential equations with jump-diffusion and piecewise continuous arguments. By combining compensated split-step methods and balanced methods, a class of compensated split-step balanced (CSSB) methods are suggested for solving the equations. Based on the one-sided Lipschitz condition and local Lipschitz condition, a strong convergence criterion of CSSB methods is derived. It is proved under some suitable conditions that the numerical solutions produced by CSSB methods can preserve the mean-square exponential stability of the corresponding analytical solutions. Several numerical examples are presented to illustrate the obtained theoretical results and the effectiveness of CSSB methods. Moreover, in order to show the computational advantage of CSSB methods, we also give a numerical comparison with the adapted split-step backward Euler methods with or without compensation and tamed explicit methods.
报告题目3：Numerical analysis of a time discretized method for nonlinear filtering problem with diffusive and point process observations
报告人：邹永魁
报告时间：2022年11月26日 14:30
报告地点：腾讯会议 ID 742-454-293
主办单位：安徽省高端装备智能控制国际联合研究中心，高端装备先进感知与智能控制教育部重点实验室，数理与金融学院，科技处，研究生部
报告人简介：邹永魁，男，1967年生人，吉林大学数学学院教授，博士生导师，2005年入选教育部新世纪人才支持计划。主要从事发展方程及分支问题数值计算方法和随机偏微分方程数值计算方法的研究。目前已在国内外有影响的学术期刊上发表论文30余篇。主持并完成了国家自然基金项目、教育部留学回国人员基金项目和吉林省科技发展计划重点项目等基金10余项。
报告摘要：In this paper we consider a nonlinear filter model with observations driven by correlated diffusive processes and point process. We first derive a Zakai equation whose solution is an unnormalized probability density function of the filter solution. Then we apply a splitting-up technique to decompose the Zakai equation into three regular easily solvable stochastic differential equations, based on which we construct a splitting-up approximate solution and derive its convergence of first order. Furthermore, we use difference method to construct a semi-discretized approximate solution of Zakai equation and prove the convergence is of half order. Finally we present some numerical experiments to demonstrate the theoretical analysis.
报告题目4：Positivity preserving logarithmic Euler-Maruyama type scheme for stochastic differential equations
报告人：赵景军
报告时间：2022年11月26日 15:00
报告地点：腾讯会议 ID 742-454-293
主办单位：安徽省高端装备智能控制国际联合研究中心，高端装备先进感知与智能控制教育部重点实验室，数理与金融学院，科技处，研究生部
报告人简介：赵景军，哈尔滨工业大学数学学院教授、博士生导师。哈尔滨工程大学兼职教授、博士生导师。曾访问剑桥大学、阿尔伯塔大学、香港大学、中科院数学与系统科学研究院。现任中国仿真学会算法委员会理事，黑龙江省工业与应用数学学会常务理事。主要从事微分方程数值解的研究。在SIAM J. Numer. Anal.和J. Sci. Comput.等期刊发表SCI论文70余篇。主持国家自然科学基金2项，参加国家自然科学基金2项、国防预研基金1项。获黑龙江省科学技术二等奖1项、中国高校自然科学二等奖1项。
报告摘要：A logarithmic truncated Euler-Maruyama method is proposed to preserve the positivity of the general stochastic differential equations. The exponential integrability is proved for both the exact solution and the numerical solution. Moreover, under some reasonable conditions, the strong convergence rate of the underlying numerical method is obtained.
报告题目5：Numerical methods for weakly singular stochastic Volterra integral equations
报告人：黄乘明
报告时间：2022年11月26日 15:30
报告地点：腾讯会议 ID 742-454-293
主办单位：安徽省高端装备智能控制国际联合研究中心，高端装备先进感知与智能控制教育部重点实验室，数理与金融学院，科技处，研究生部
报告人简介：黄乘明，华中科技大学教授（二级）、博士生导师；兼任中国数学会计算数学分会常务理事；曾经和现任J Comput Appl Math、J Frankl Inst等4个SCI期刊编委。主要从事微分方程数值计算研究，主持国家自然科学基金项目7项，在SINUM、SISC、Numer Math、IMAJNA、JCP、JSC等学术期刊发表SCI论文100余篇。
报告摘要：In this talk we first establish the existence, uniqueness and Holder continuity of the solution to stochastic Volterra integral equations (SVIEs) with weakly singular kernels, with singularities α ∈ (0, 1) for the drift term and β ∈ (0, 1/2) for the stochastic term. Subsequently, we propose a θ-Euler–Maruyama scheme and a Milstein scheme to solve the equations numerically and obtain strong rates of convergence for both schemes in Lp norm for any p ≥1. For the Theta-Euler–Maruyama scheme the rate is min{1−α, 1/2−β} and for the Milstein scheme is min{1−α, 1−2β}. These results on the rates of convergence are significantly different from those it is similar schemes for the SVIEs with regular kernels. This talk is based on the joint work with Dr. Min Li and Professor Yaozhong Hu.
报告题目6：Singular stochastic Volterra integral equations: Well-posedness and numerical approximation
报告人：肖爱国
报告时间：2022年11月26日 16:00
报告地点：腾讯会议 ID 742-454-293
主办单位：安徽省高端装备智能控制国际联合研究中心，高端装备先进感知与智能控制教育部重点实验室，数理与金融学院，科技处，研究生部
报告人简介：肖爱国，现任湘潭大学数学与计算科学学院教授、湖南省级重点实验室主任、中国仿真学会仿真算法专业委员会主任委员、中国数学会计算数学分会委员会常务理事、《数值计算与计算机应用》编委等。1999年在北京应用物理与计算数学研究所获博士学位，2001年从中国科学院计算数学与科学工程计算研究所博士后出站。长期从事微分方程数值方法研究，主持国家863课题和国家自然科学基金面上项目6项等，在知名SCI刊物上发表论文80多篇，获湖南省和教育部自然科学二等奖及国家教学成果二等奖、湖南省教学成果一等奖、宝钢教育奖优秀教师奖、湖南省优秀研究生导师等。
报告摘要：This talk focus on three classes of stochastic Volterra integral equations with weakly singular kernels from the perspective of well-posedness and numerical approximation.
1) For the stochastic fractional integro-differential equation with weakly singular kernels, it can be rewritten as an equivalent stochastic Volterra integral equation. We prove the well-posedness of the exact solution, the strong convergence of Euler-Maruyama (EM) approximation under local Lipschitz continuous and linear growth condition, and the strong convergence rate of EM approximation under global Lipschitz continuous and linear growth condition.
2) For Lévy-driven stochastic Volterra integral equations with doubly singular kernels, we prove the well-posedness of the exact solution under local Lipschitz continuous and linear growth condition, and propose a fast EM method based on the sum-of-exponentials approximation, which improves the computational cost and efficiency of EM methods.
3) For the overdamped generalized Langevin equation with fractional noise, we extend the existing convergence result of the Euler method to general parameter cases by delicately treating the singular stochastic integral with respect to fractional Brownian motion.
报告题目7：Strong and weak convergence rates of logarithmic transformed truncated EM methods for SDEs with positive
报告人：甘四清
报告时间：2022年11月26日 16:30
报告地点：腾讯会议 ID 742-454-293
主办单位：安徽省高端装备智能控制国际联合研究中心，高端装备先进感知与智能控制教育部重点实验室，数理与金融学院，科技处，研究生部
报告人简介：甘四清，博士，中南大学教授，博士生导师。2001年毕业于中国科学院数学研究所，获理学博士学位，2001-2003年在清华大学计算机科学与技术系高性能计算研究所从事博士后研究工作。主要研究方向为确定性微分方程和随机微分方程数值解法。主持国家自然科学基金面上项目4项， 参加国家自然科学基金重大研究计划集成项目1项，参加国家自然科学基金项目多项。在《SIAM Journal on Scientific Computing》、《Journal of Scientific Computing》、《BIT Numerical Analysis》、《Applied Numerical Mathematics》、《Journal of Mathematics Analysis and Applications》、《中国科学》等国内外学术刊物上发表论文90余篇。2005年入选湖南省首批新世纪121人才工程。2014年湖南省优秀博士学位论文指导老师。
报告摘要：To inherit numerically the positivity of stochastic differential equations (SDEs) with non-globally Lipschitz coefficients, we devise a novel explicit method, called logarithmic transformed truncated Euler-Maruyama method. There is however a price to be paid for the preserving positivity, namely that the logarithmic transformation would cause the coefficients of the transformed SDEs growing super-linearly or even exponentially, which makes the strong and weak convergence analysis more complicated. Based on the exponential integrability, truncation techniques and some other arguments, we show that the strong convergence rate of the underlying numerical method is 1/2, and the weak convergence rate can be arbitrarily close to 1. To the best of our knowledge, this is the first result establishing the weak convergence rate of numerical methods for the general SDEs with positive solutions. Numerical experiments are finally reported to confirm our theoretical results.
报告题目8：Central limit theorems for approximating ergodic limit of SPDEs via a full discretization
报告人：陈楚楚
报告时间：2022年11月26日 17:00
报告地点：腾讯会议 ID 742-454-293
主办单位：安徽省高端装备智能控制国际联合研究中心，高端装备先进感知与智能控制教育部重点实验室，数理与金融学院，科技处，研究生部
报告人简介：陈楚楚，中国科学院数学与系统科学研究院，副研究员。2015年在数学与系统科学研究院获博士学位，2015-2017年先后在普渡大学和密歇根州立大学从事博士后研究工作。主要研究方向为随机偏微分方程保结构算法及其理论分析。
报告摘要：In this talk, we focus on characterizing quantitatively the fluctuations between the ergodic limit and the time-averaging estimator of the full discretization for the parabolic stochastic partial differential equation. We establish a central limit theorem, which shows that the normalized time-averaging estimator converges to a normal distribution with the variance being the same as that of the continuous case, where the scale used for the normalization corresponds to the temporal strong convergence rate of the considered full discretization.
报告题目9：Regime-switching diffusion processes with infinite delay
报告人：席福宝
报告时间：2022年11月26日 18:30
报告地点：腾讯会议 ID 742-454-293
主办单位：安徽省高端装备智能控制国际联合研究中心，高端装备先进感知与智能控制教育部重点实验室，数理与金融学院，科技处，研究生部
报告人简介：席福宝，北京理工大学教授，博士生导师。担任中国概率统计学会理事，中国工程概率统计学会常务理事，美国《Math. Reviews》评论员。主要从事马氏过程与随机分析领域的研究工作，特别地，关于含小参数的切换扩散过程的大偏差，切换跳扩散过程的随机稳定性、Feller性、强Feller性、指数遍历性、强遍历性以及收敛速度估计等方面，取得了一系列重要研究成果；在SIAM Journal on Control and Optimization, Stochastic Processes and their Applications, Journal of Differential Equations, Journal of Applied Probability, Science China Mathematics等国内外重要学术期刊上发表论文60余篇。
报告摘要：In this work we consider a class of regime-switching diffusion processes, which are determined by solutions X(t) to stochastic functional differential equation with infinite delay and random switching represented by jump process \Lambda(t). We first establish the existence and uniqueness of the underlying process by an interlacing procedure. Under suitable conditions, we then investigate convergence and boundedness of both the solution X(t) and the solution map X_{t}. We show that two solutions (resp. solution maps) from different initial data living in the same initial switching regime will be close with high probability as time variable tends to infinity, and that the solution (resp. solution map) is uniformly bounded in the mean square sense. Moreover, we prove existence and uniqueness of the invariant probability measure of two-component Markov-Feller process (X_{t}, \Lambda(t)), and establish exponential bounds on the rate of convergence to the invariant probability measure under Wasserstein distance. Finally, we provide a concrete example to illustrate our main results.
报告题目10：Ergodicity and stability of hybrid systems with threshold type state-dependent switching
报告人：邵井海
报告时间：2022年11月26日 19:00
报告地点：腾讯会议 ID 742-454-293
主办单位：安徽省高端装备智能控制国际联合研究中心，高端装备先进感知与智能控制教育部重点实验室，数理与金融学院，科技处，研究生部
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。2006年获得北京师范大学与法国第戎大学的理学博士学位。邵井海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，在轨道空间和环空间上运输不等式、Monge-Kantorovich最优映射问题，以及带切换扩散过程长时间行为等问题的研究中取得了一些成果。
报告摘要：To deal with stochastic hybrid systems with general state-dependent switching, we propose an approximation method by a sequence of stochastic hybrid systems with threshold type switching. The convergence rate in the Wasserstein distance is estimated in terms of the difference between transition rate matrices. Our method is based on an elaborate construction of coupling processes in terms of Skorokhod's representation theorem for jumping processes. Moreover, we establish explicit criteria on the ergodicity and stability for stochastic hybrid systems with threshold type switching. Some examples are given to illustrate the sharpness of these criteria.
报告题目11：Uniform Poincare inequalities and logarithmic Sobolev inequalities for mean field particle systems
报告人：刘伟
报告时间：2022年11月26日 19：30
报告地点：腾讯会议 ID 742-454-293
主办单位：安徽省高端装备智能控制国际联合研究中心，高端装备先进感知与智能控制教育部重点实验室，数理与金融学院，科技处，研究生部
报告人简介：刘伟，武汉大学数学与统计学院，教授，博士生导师。1999年进入武汉大学数学基地班学习，2003年免试攻读硕士研究生(硕博连读，师从吴黎明教授)，读博期间曾在法国进行博士联合培养，2009年博士毕业留校任教。2017年至2019年受留学基金委资助在法国公派访学。目前主要从事随机分析和随机算法方面的研究，主持国家自科面上项目，参与承担多项国家自科重点项目和面上项目，在CMP、JMPA、AOAP、SPA、AIHP、Science in China 等国内外一流学术期刊发表学术论文，担任多家过国内外期刊审稿人。
报告摘要：In this talk we show some explicit and sharp estimates of the spectral gap and the log-Sobolev constant for mean field particles system, uniform in the number of particles, when the confinement potential have many local minimums. Our uniform log-Sobolev inequality, based on Zegarlinski‘s theorem for Gibbs measures, allows us to obtain the exponential convergence in entropy of the McKean-Vlasov equation with an explicit rate constant, generalizing the result of Carrillo-McCann-Villani(2003) by means of the displacement convexity approach, or Malrieu(2001,2003) by Bakry-Emery technique or the recent work of Bolley-Gentil-Guillin by dissipation of the Wasserstein distance.This talk is based on a joint work with Arnaud Guillin, Liming Wu and Chaoen Zhang.
报告题目12：A probability approximation framework and its applications
报告人：徐礼虎
报告时间：2022年11月26日 20:00
报告地点：腾讯会议 ID 742-454-293
主办单位：安徽省高端装备智能控制国际联合研究中心，高端装备先进感知与智能控制教育部重点实验室，数理与金融学院，科技处，研究生部
报告人简介：徐礼虎博士毕业于帝国理工学院，现为澳门大学副教授，主要研究方向是随机过程及其在算法上的应用。目前在Annals of Statistics, Probability Theory and Related Fields, Annals of Applied Probability, Bernoulli, Journal of Functional Analysis, Stochastic Processes and Their Applications等杂志发表40余篇论文。
报告摘要：By embedding the classical Lindeberg principle into a Markov process and using conditional expectation, we establish a general probability approximation framework. As applications, we study the error bounds of the following three approximations: approximating online stochastic gradient descents (SGDs) by stochastic differential equations (SDEs), approximating stochastic variance reduced gradients (SVRGs) by stochastic differential delay equations (SDDEs), and the approximation of ergodic measure of stable SDEs by Euler-Maruyama scheme. More applications will be discussed. This talk is based on the joint works with P. Chen, J. Lu, X. Jin, and Q. M. Shao.
报告题目13：The convergence rate of the equilibrium measure for the LQG mean field game with a common noise
报告人：宋庆硕
报告时间：2022年11月26日 20:30
报告地点：腾讯会议 ID 742-454-293
主办单位：安徽省高端装备智能控制国际联合研究中心，高端装备先进感知与智能控制教育部重点实验室，数理与金融学院，科技处，研究生部
报告人简介：Qingshuo Song's research interests include stochastic control theory and its applications to mathematical finance and various engineering problems. Qingshuo received his BSc from Nankai University and his Ph.D. from Wayne State University. Prior to joining Worcester Polytechnic Institute, he worked with the City University of Hong Kong (Associate Professor 2010-2018), the University of Michigan (PostDoc 2009), and the University of Southern California (PostDoc 2006-2009). He is currently an associate professor and doctoral supervisor at Worcester Polytechnic Institute, USA.
报告摘要：The convergence rate of equilibrium measures of N-player Games with Brownian common noise to its asymptotic Mean Field Game system is known as 1/9 with respect to 1-Wasserstein distance, obtained by the monograph [6, Cardaliaguet, Delarue, Lasry, Lions (2019)]. In this work, we study the convergence rate of the N-player LQG game with a Markov chain common noise towards its asymptotic Mean Field Game. The approach relies on an explicit coupling of the optimal trajectory of the N-player game driven by N-dimensional Brownian motion and the Mean Field Game counterpart driven by one-dimensional Brownian motion. As a result, the convergence rate is 1/2 with respect to the 2-Wasserstein distance. It's joint work with Jiamin Jian, Peiyao Lai, and Jiaxuan Ye.
报告题目14：Mean square stability of stochastic theta method for stochastic differential equations driven by fractional Brownian motion
报告人：胡耀忠
报告时间：2022年11月26日 21:00
报告地点：腾讯会议 ID 742-454-293
主办单位：安徽省高端装备智能控制国际联合研究中心，高端装备先进感知与智能控制教育部重点实验室，数理与金融学院，科技处，研究生部
报告人简介：Yaozhong Hu obtained his Ph.D in 1992 from Strasbourg University under the supervision of Paul Andre Meyer. He made significant contributions to stochastic analysis, fractional Brownian motions, stochastic partial differential equations and Malliavin calculus. He is currently a centennial professor and doctoral supervisor at University of Alberta at Edmonton, Canada.
报告摘要：I will present a result on the mean square stability of the solution and its stochastic theta scheme for the linear stochastic differential equations driven by fractional Brownian motion with Hurst parameter 1/2<H<1.
报告题目15：Positivity and boundedness preserving numerical scheme for the stochastic epidemic model
报告人：毛学荣
报告时间：2022年11月26日 21:30
报告地点：腾讯会议 ID 742-454-293
主办单位：安徽省高端装备智能控制国际联合研究中心，高端装备先进感知与智能控制教育部重点实验室，数理与金融学院，科技处，研究生部
报告人简介：毛学荣是英国斯克莱德大学数学与统计系教授、爱丁堡皇家学会（即苏格兰皇家学院）院士。也是“长江讲座教授”和“英国沃弗森研究功勋奖”获得者。 近日，Guide2Research发布了全球数学领域顶尖科学家榜单，他列英国第1位，全球第93位。他是国际知名的随机稳定性和随机控制领域的专家，在该领域做出了杰出的贡献，享有很高的声誉。他擅长随机分析，随机系统数值计算，在对随机系统处理方面，提出了系列处理方法与技巧，很有特色，被广泛采用。例如，对噪声镇定给出了科学的理论，被后续跟踪者所广泛推崇；在随机人口/疾病模型理论方面做出了突出的贡献；在随机系统LaSalle原理方面做出了开拓性的工作；奠定了随机跳变系统理论方面的研究。目前，他致力于推动超线性随机系统的理论研究和数值计算，难度大，挑战性强。近年来，他受各国同行邀请，奔忙于世界各地，讲学、开展合作。在中国，他与上海师范大学、东北师范大学，东华大学、华中科技大学、 、香港大学等校同行开展了系列的合作，培养了一大批年轻学者（教师、学生），影响了一大批同行与后辈。
报告摘要：
This work concerns about the numerical solution to the stochastic epidemic model proposed by Cai et al. in 2019. The typical features of the model including the positivity and boundedness of the solution and the presence of the square-root diffusion term make this an interesting and challenging work. By modifying the classical Euler-Maruyama (EM) scheme, we generate a positivity and boundedness preserving numerical scheme, which is proved to have a strong convergence to the true solution over finite time intervals. We also demonstrate that the principle of this method is applicable to a bunch of popular stochastic differential equation (SDE) models, e.g. the mean-reverting square-root process, an important financial model, and the multi-dimensional SDE SIR epidemic model. This is a joint work with Y. Cai and J. Hu.