報告題目1：A frequency domain for the stabilizing feedback controller of linear delay systems
報告人：胡廣大
報告時間：2022年11月26日 13:30
報告地點：騰訊會議 ID 742-454-293
主辦單位：安徽省高端裝備智能控制國際聯(lián)合研究中心,，高端裝備先進感知與智能控制教育部重點實驗室,，數(shù)理與金融學(xué)院，科技處,，研究生部
報告人簡介：胡廣大, 上海大學(xué)數(shù)學(xué)系教授,，博導(dǎo)，運籌學(xué)與控制論研究所所長,。1996獲得日本國名古屋大學(xué)計算機科學(xué)系博士,， 1999-2000年加拿大紐芬蘭大學(xué)計算機科學(xué)系博士后。曾訪問英國曼徹斯特大學(xué),，加拿大約克大學(xué),。先后任教于哈爾濱工業(yè)大學(xué)和北京科技大學(xué)。2011年以來至今,，任國際SCI雜志“Journal of Computational and Applied Mathematics”編委,。主要研究方向是控制系統(tǒng)設(shè)計的數(shù)值最優(yōu)化方法和.微分方程的數(shù)值分析。研究成果分別被意大利和美國學(xué)者的專著收錄為定理,。于2006年獲得黑龍江省科技進步一等獎（自然科學(xué)類）以及全球前2%頂尖科學(xué)家榜單,。主持國家自然科學(xué)基金5項和教育部博士點基金1項。在IEEE Trans. Automatic Control, IEEE Trans. Signal Processing, International Journal of Control,，BIT Numeral Mathematics,，J. Comput. Appl. Math.，等國際SCI雜志上發(fā)表論文70多篇,。由Springer出版英文教材一部,。
報告摘要：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.
報告題目2：Compensated split-step balanced methods for nonlinear stiff SDEs with jump-diffusion and piecewise continuous arguments
報告人：張誠堅
報告時間：2022年11月26日 14:00
報告地點：騰訊會議 ID 742-454-293
主辦單位：安徽省高端裝備智能控制國際聯(lián)合研究中心，高端裝備先進感知與智能控制教育部重點實驗室,，數(shù)理與金融學(xué)院,，科技處，研究生部
報告人簡介：張誠堅, 華中科技大學(xué)二級教授, 博士生導(dǎo)師. 1998年畢業(yè)于湖南大學(xué)應(yīng)用數(shù)學(xué)專業(yè)獲理學(xué)博士學(xué)位后, 調(diào)入華中理工大學(xué)數(shù)學(xué)系,，并同時進入該?？刂瓶茖W(xué)與工程博士后流動站工作(2000年出站). 2002年2月至2004年3月在比利時魯汶大學(xué)計算機科學(xué)系做合作研究工作.曾擔(dān)任華中科技大學(xué)數(shù)學(xué)與統(tǒng)計學(xué)院院長、中國數(shù)學(xué)學(xué)會第十屆,、十一屆理事,、中國計算數(shù)學(xué)學(xué)會第七屆、八屆常務(wù)理事及湖北省數(shù)學(xué)學(xué)會副理事長. 現(xiàn)兼任中國仿真算法專業(yè)委員會副主任委員,、中國數(shù)學(xué)學(xué)會奇異攝動專業(yè)委員會委員,、湖北省工程建模與科學(xué)計算重點實驗室主任、《Applied Mathematics and Computation》副主編及《Mathematics and Computers in Simulation》,、《Acta Mathematica Scientia》等國際學(xué)術(shù)期刊編委.主要從事剛性時滯微分方程數(shù)值解及其算法理論研究,，主持有國家自然科學(xué)基金面上項目6項,、教育部留學(xué)回國人員啟動基金及湖北省自然科學(xué)基金各1項，并作為主要成員承擔(dān)過國家自然科學(xué)基金重大研究計劃課題和國家高技術(shù)研究發(fā)展計劃重點項目. 在《SIAM J. Sci. Comput.》,、《IMA J. Numer. Anal. 》,、《Numer. Math.》等國內(nèi)外學(xué)術(shù)期刊發(fā)表SCI收錄論文100余篇，主,、參編教材5部,，主持有國家級精品課程及國家級精品資源共享課《計算方法》. 曾獲國務(wù)院政府特殊津貼、機械工業(yè)部科技進步二等獎,、湖北省自然科學(xué)獎二等獎,、湖北省有突出貢獻的中青年專家、寶鋼優(yōu)秀教師獎,、湖北省優(yōu)秀教學(xué)成果一等獎及湖北省優(yōu)秀教育工作者等.
報告摘要：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.
報告題目3：Numerical analysis of a time discretized method for nonlinear filtering problem with diffusive and point process observations
報告人：鄒永魁
報告時間：2022年11月26日 14:30
報告地點：騰訊會議 ID 742-454-293
主辦單位：安徽省高端裝備智能控制國際聯(lián)合研究中心,，高端裝備先進感知與智能控制教育部重點實驗室，數(shù)理與金融學(xué)院,，科技處,，研究生部
報告人簡介：鄒永魁，男,，1967年生人,，吉林大學(xué)數(shù)學(xué)學(xué)院教授，博士生導(dǎo)師,，2005年入選教育部新世紀(jì)人才支持計劃,。主要從事發(fā)展方程及分支問題數(shù)值計算方法和隨機偏微分方程數(shù)值計算方法的研究。目前已在國內(nèi)外有影響的學(xué)術(shù)期刊上發(fā)表論文30余篇,。主持并完成了國家自然基金項目,、教育部留學(xué)回國人員基金項目和吉林省科技發(fā)展計劃重點項目等基金10余項。
報告摘要：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.
報告題目4：Positivity preserving logarithmic Euler-Maruyama type scheme for stochastic differential equations
報告人：趙景軍
報告時間：2022年11月26日 15:00
報告地點：騰訊會議 ID 742-454-293
主辦單位：安徽省高端裝備智能控制國際聯(lián)合研究中心,，高端裝備先進感知與智能控制教育部重點實驗室,，數(shù)理與金融學(xué)院，科技處,，研究生部
報告人簡介：趙景軍,，哈爾濱工業(yè)大學(xué)數(shù)學(xué)學(xué)院教授、博士生導(dǎo)師,。哈爾濱工程大學(xué)兼職教授,、博士生導(dǎo)師。曾訪問劍橋大學(xué),、阿爾伯塔大學(xué),、香港大學(xué)、中科院數(shù)學(xué)與系統(tǒng)科學(xué)研究院?，F(xiàn)任中國仿真學(xué)會算法委員會理事,，黑龍江省工業(yè)與應(yīng)用數(shù)學(xué)學(xué)會常務(wù)理事,。主要從事微分方程數(shù)值解的研究。在SIAM J. Numer. Anal.和J. Sci. Comput.等期刊發(fā)表SCI論文70余篇,。主持國家自然科學(xué)基金2項,，參加國家自然科學(xué)基金2項、國防預(yù)研基金1項,。獲黑龍江省科學(xué)技術(shù)二等獎1項,、中國高校自然科學(xué)二等獎1項。
報告摘要：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.
報告題目5：Numerical methods for weakly singular stochastic Volterra integral equations
報告人：黃乘明
報告時間：2022年11月26日 15:30
報告地點：騰訊會議 ID 742-454-293
主辦單位：安徽省高端裝備智能控制國際聯(lián)合研究中心,，高端裝備先進感知與智能控制教育部重點實驗室,，數(shù)理與金融學(xué)院，科技處,，研究生部
報告人簡介：黃乘明，華中科技大學(xué)教授（二級）,、博士生導(dǎo)師,；兼任中國數(shù)學(xué)會計算數(shù)學(xué)分會常務(wù)理事；曾經(jīng)和現(xiàn)任J Comput Appl Math,、J Frankl Inst等4個SCI期刊編委,。主要從事微分方程數(shù)值計算研究，主持國家自然科學(xué)基金項目7項,，在SINUM,、SISC、Numer Math,、IMAJNA,、JCP、JSC等學(xué)術(shù)期刊發(fā)表SCI論文100余篇,。
報告摘要：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.
報告題目6：Singular stochastic Volterra integral equations: Well-posedness and numerical approximation
報告人：肖愛國
報告時間：2022年11月26日 16:00
報告地點：騰訊會議 ID 742-454-293
主辦單位：安徽省高端裝備智能控制國際聯(lián)合研究中心,，高端裝備先進感知與智能控制教育部重點實驗室，數(shù)理與金融學(xué)院,，科技處,，研究生部
報告人簡介：肖愛國，現(xiàn)任湘潭大學(xué)數(shù)學(xué)與計算科學(xué)學(xué)院教授,、湖南省級重點實驗室主任,、中國仿真學(xué)會仿真算法專業(yè)委員會主任委員、中國數(shù)學(xué)會計算數(shù)學(xué)分會委員會常務(wù)理事,、《數(shù)值計算與計算機應(yīng)用》編委等,。1999年在北京應(yīng)用物理與計算數(shù)學(xué)研究所獲博士學(xué)位，2001年從中國科學(xué)院計算數(shù)學(xué)與科學(xué)工程計算研究所博士后出站,。長期從事微分方程數(shù)值方法研究,，主持國家863課題和國家自然科學(xué)基金面上項目6項等,，在知名SCI刊物上發(fā)表論文80多篇，獲湖南省和教育部自然科學(xué)二等獎及國家教學(xué)成果二等獎,、湖南省教學(xué)成果一等獎,、寶鋼教育獎優(yōu)秀教師獎、湖南省優(yōu)秀研究生導(dǎo)師等,。
報告摘要：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.
報告題目7：Strong and weak convergence rates of logarithmic transformed truncated EM methods for SDEs with positive
報告人：甘四清
報告時間：2022年11月26日 16:30
報告地點：騰訊會議 ID 742-454-293
主辦單位：安徽省高端裝備智能控制國際聯(lián)合研究中心,，高端裝備先進感知與智能控制教育部重點實驗室，數(shù)理與金融學(xué)院,，科技處,，研究生部
報告人簡介：甘四清，博士,，中南大學(xué)教授,，博士生導(dǎo)師。2001年畢業(yè)于中國科學(xué)院數(shù)學(xué)研究所,，獲理學(xué)博士學(xué)位,，2001-2003年在清華大學(xué)計算機科學(xué)與技術(shù)系高性能計算研究所從事博士后研究工作。主要研究方向為確定性微分方程和隨機微分方程數(shù)值解法,。主持國家自然科學(xué)基金面上項目4項,， 參加國家自然科學(xué)基金重大研究計劃集成項目1項，參加國家自然科學(xué)基金項目多項,。在《SIAM Journal on Scientific Computing》,、《Journal of Scientific Computing》、《BIT Numerical Analysis》,、《Applied Numerical Mathematics》,、《Journal of Mathematics Analysis and Applications》、《中國科學(xué)》等國內(nèi)外學(xué)術(shù)刊物上發(fā)表論文90余篇,。2005年入選湖南省首批新世紀(jì)121人才工程,。2014年湖南省優(yōu)秀博士學(xué)位論文指導(dǎo)老師。
報告摘要：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.
報告題目8：Central limit theorems for approximating ergodic limit of SPDEs via a full discretization
報告人：陳楚楚
報告時間：2022年11月26日 17:00
報告地點：騰訊會議 ID 742-454-293
主辦單位：安徽省高端裝備智能控制國際聯(lián)合研究中心,，高端裝備先進感知與智能控制教育部重點實驗室,，數(shù)理與金融學(xué)院，科技處,，研究生部
報告人簡介：陳楚楚,，中國科學(xué)院數(shù)學(xué)與系統(tǒng)科學(xué)研究院，副研究員,。2015年在數(shù)學(xué)與系統(tǒng)科學(xué)研究院獲博士學(xué)位,，2015-2017年先后在普渡大學(xué)和密歇根州立大學(xué)從事博士后研究工作。主要研究方向為隨機偏微分方程保結(jié)構(gòu)算法及其理論分析。
報告摘要：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.
報告題目9：Regime-switching diffusion processes with infinite delay
報告人：席福寶
報告時間：2022年11月26日 18:30
報告地點：騰訊會議 ID 742-454-293
主辦單位：安徽省高端裝備智能控制國際聯(lián)合研究中心,，高端裝備先進感知與智能控制教育部重點實驗室,，數(shù)理與金融學(xué)院，科技處,，研究生部
報告人簡介：席福寶,，北京理工大學(xué)教授，博士生導(dǎo)師,。擔(dān)任中國概率統(tǒng)計學(xué)會理事,，中國工程概率統(tǒng)計學(xué)會常務(wù)理事，美國《Math. Reviews》評論員,。主要從事馬氏過程與隨機分析領(lǐng)域的研究工作,，特別地，關(guān)于含小參數(shù)的切換擴散過程的大偏差,，切換跳擴散過程的隨機穩(wěn)定性,、Feller性、強Feller性,、指數(shù)遍歷性,、強遍歷性以及收斂速度估計等方面，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等國內(nèi)外重要學(xué)術(shù)期刊上發(fā)表論文60余篇。
報告摘要：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.
報告題目10：Ergodicity and stability of hybrid systems with threshold type state-dependent switching
報告人：邵井海
報告時間：2022年11月26日 19:00
報告地點：騰訊會議 ID 742-454-293
主辦單位：安徽省高端裝備智能控制國際聯(lián)合研究中心,，高端裝備先進感知與智能控制教育部重點實驗室,，數(shù)理與金融學(xué)院，科技處,，研究生部
報告人簡介：邵井海,，天津大學(xué)應(yīng)用數(shù)學(xué)中心教授，博士生導(dǎo)師,。2006年獲得北京師范大學(xué)與法國第戎大學(xué)的理學(xué)博士學(xué)位,。邵井海主要從事概率論遍歷性理論、隨機分析,、隨機微分方程方面的研究工作,，在軌道空間和環(huán)空間上運輸不等式、Monge-Kantorovich最優(yōu)映射問題,，以及帶切換擴散過程長時間行為等問題的研究中取得了一些成果,。
報告摘要：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.
報告題目11：Uniform Poincare inequalities and logarithmic Sobolev inequalities for mean field particle systems
報告人：劉偉
報告時間：2022年11月26日 19：30
報告地點：騰訊會議 ID 742-454-293
主辦單位：安徽省高端裝備智能控制國際聯(lián)合研究中心，高端裝備先進感知與智能控制教育部重點實驗室,，數(shù)理與金融學(xué)院,，科技處，研究生部
報告人簡介：劉偉，武漢大學(xué)數(shù)學(xué)與統(tǒng)計學(xué)院,，教授,，博士生導(dǎo)師。1999年進入武漢大學(xué)數(shù)學(xué)基地班學(xué)習(xí),，2003年免試攻讀碩士研究生(碩博連讀,，師從吳黎明教授)，讀博期間曾在法國進行博士聯(lián)合培養(yǎng),，2009年博士畢業(yè)留校任教,。2017年至2019年受留學(xué)基金委資助在法國公派訪學(xué)。目前主要從事隨機分析和隨機算法方面的研究,，主持國家自科面上項目,，參與承擔(dān)多項國家自科重點項目和面上項目，在CMP,、JMPA,、AOAP、SPA,、AIHP,、Science in China 等國內(nèi)外一流學(xué)術(shù)期刊發(fā)表學(xué)術(shù)論文，擔(dān)任多家過國內(nèi)外期刊審稿人,。
報告摘要：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.
報告題目12：A probability approximation framework and its applications
報告人：徐禮虎
報告時間：2022年11月26日 20:00
報告地點：騰訊會議 ID 742-454-293
主辦單位：安徽省高端裝備智能控制國際聯(lián)合研究中心,，高端裝備先進感知與智能控制教育部重點實驗室，數(shù)理與金融學(xué)院,，科技處,，研究生部
報告人簡介：徐禮虎博士畢業(yè)于帝國理工學(xué)院，現(xiàn)為澳門大學(xué)副教授,，主要研究方向是隨機過程及其在算法上的應(yīng)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等雜志發(fā)表40余篇論文。
報告摘要：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.
報告題目13：The convergence rate of the equilibrium measure for the LQG mean field game with a common noise
報告人：宋慶碩
報告時間：2022年11月26日 20:30
報告地點：騰訊會議 ID 742-454-293
主辦單位：安徽省高端裝備智能控制國際聯(lián)合研究中心,，高端裝備先進感知與智能控制教育部重點實驗室,，數(shù)理與金融學(xué)院，科技處,，研究生部
報告人簡介：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.
報告摘要：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.
報告題目14：Mean square stability of stochastic theta method for stochastic differential equations driven by fractional Brownian motion
報告人：胡耀忠
報告時間：2022年11月26日 21:00
報告地點：騰訊會議 ID 742-454-293
主辦單位：安徽省高端裝備智能控制國際聯(lián)合研究中心,，高端裝備先進感知與智能控制教育部重點實驗室，數(shù)理與金融學(xué)院,，科技處,，研究生部
報告人簡介：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.
報告摘要：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.
報告題目15：Positivity and boundedness preserving numerical scheme for the stochastic epidemic model
報告人：毛學(xué)榮
報告時間：2022年11月26日 21:30
報告地點：騰訊會議 ID 742-454-293
主辦單位：安徽省高端裝備智能控制國際聯(lián)合研究中心，高端裝備先進感知與智能控制教育部重點實驗室,，數(shù)理與金融學(xué)院,，科技處,，研究生部
報告人簡介：毛學(xué)榮是英國斯克萊德大學(xué)數(shù)學(xué)與統(tǒng)計系教授、愛丁堡皇家學(xué)會（即蘇格蘭皇家學(xué)院）院士,。也是“長江講座教授”和“英國沃弗森研究功勛獎”獲得者,。 近日，Guide2Research發(fā)布了全球數(shù)學(xué)領(lǐng)域頂尖科學(xué)家榜單,，他列英國第1位,，全球第93位。他是國際知名的隨機穩(wěn)定性和隨機控制領(lǐng)域的專家,，在該領(lǐng)域做出了杰出的貢獻,，享有很高的聲譽。他擅長隨機分析,，隨機系統(tǒng)數(shù)值計算,，在對隨機系統(tǒng)處理方面，提出了系列處理方法與技巧,，很有特色,，被廣泛采用。例如,，對噪聲鎮(zhèn)定給出了科學(xué)的理論,，被后續(xù)跟蹤者所廣泛推崇；在隨機人口/疾病模型理論方面做出了突出的貢獻,；在隨機系統(tǒng)LaSalle原理方面做出了開拓性的工作,；奠定了隨機跳變系統(tǒng)理論方面的研究。目前,，他致力于推動超線性隨機系統(tǒng)的理論研究和數(shù)值計算,，難度大，挑戰(zhàn)性強,。近年來，他受各國同行邀請,，奔忙于世界各地,，講學(xué)、開展合作,。在中國,，他與上海師范大學(xué)、東北師范大學(xué),，東華大學(xué),、華中科技大學(xué)、安徽工程大學(xué),、香港大學(xué)等校同行開展了系列的合作,，培養(yǎng)了一大批年輕學(xué)者（教師、學(xué)生），影響了一大批同行與后輩,。
報告摘要：
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.
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數(shù)理與金融學(xué)院 地址：安徽蕪湖市北京中路 郵編：241000 電話0553-2871142
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