研究领域
刘暐的研究兴趣主要在随机微分方程的数值逼近,随机偏微分方程以及随机控制这三个方向。对于随机微分方程的数值逼近,他主要关注针对非线性方程的数值方法的有限时间收敛性以及数值解的渐近性。对于随机偏微分方程,他目前关注的是白噪声和彩色噪声驱动的随机热方程的渐近性。随机控制方面,他的兴趣在于如何利用离散时间的观测值构造控制项
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14.Liu,Wei;Mao,Xuerong;Tang,Jingwen;Wu,Yue;TruncatedEuler-Maruyamamethodforaclassofnon-autonomousstochasticdifferentialequations,AppliedNumericalMathematics,2020,153:66-81.
13.Weng,Lihui;Liu,Wei;InvariantmeasuresoftheMilsteinmethodforstochasticdifferentialequationswithcommutativenoise,AppliedMathematicsandComputation,2019,358:169-176.
12.Deng,Shounian;Fei,Weiyin;Liu,Wei;Mao,Xuerong;ThetruncatedEMmethodforstochasticdifferentialequationswithPoissonjumps,JournalofComputationalandAppliedMathematics,2019,355:232-257.
11.Jiang,Yanan;Huang,Zequan;Liu,Wei;EquivalenceofthemeansquarestabilitybetweenthepartiallytruncatedEuler-Maruyamamethodandstochasticdifferentialequationswithsuper-lineargrowingcoefficients,AdvancesinDifferenceEquations,2018,355:1-15.
10.Guo,Qian;Liu,Wei;Mao,Xuerong;Zhan,Weijun;Multi-levelMonteCarlomethodswiththetruncatedEuler–Maruyamaschemeforstochasticdifferentialequations,InternationalJournalofComputerMathematics,2018,95(9):1715-1726.
9.Guo,Qian;Liu,Wei;Mao,Xuerong;AnoteonthepartiallytruncatedEuler-Maruyamamethod,AppliedNumericalMathematics,2018,130:157-170.
8.Guo,Qian;Liu,Wei;Mao,Xuerong;Yue,Rongxian;ThetruncatedMilsteinmethodforstochasticdifferentialequationswithcommutativenoise,JournalofComputationalandAppliedMathematics,2018,338:298-310.
7.Liu,Wei;Mao,Xuerong;AlmostsurestabilityoftheEuler–Maruyamamethodwithrandomvariablestepsizeforstochasticdifferentialequations,NumericalAlgorithms,2017,74(2):573-592.
6.Guo,Qian;Liu,Wei;Mao,Xuerong;Yue,Rongxian;ThepartiallytruncatedEuler–Maruyamamethodanditsstabilityandboundedness,AppliedNumericalMathematics,2017,115:235-251.
5.Liu,Wei;Mao,Xuerong;Numericalstationarydistributionanditsconvergencefornonlinearstochasticdifferentialequations,JournalofComputationalandAppliedMathematics,2015,276:16-29.
4.Qiu,Qinwei;Liu,Wei;Hu,Liangjian;Asymptoticmomentboundednessofthestochasticthetamethodanditsapplicationforstochasticdifferentialequations,AdvancesinDifferenceEquations,2014,310:1-14.
3.Liu,Wei;Foondun,Mohammud;Mao,Xuerong;Meansquarepolynomialstabilityofnumericalsolutionstoaclassofstochasticdifferentialequations,StatisticsandProbabilityLetters,2014,92:173-182.
2.Liu,Wei;Mao,Xuerong;StrongconvergenceofthestoppedEuler–Maruyamamethodfornonlinearstochasticdifferentialequations,AppliedMathematicsandComputation,2013,223:389-400.
1.Liu,Wei;Mao,Xuerong;Asymptoticmomentboundednessofthenumericalsolutionsofstochasticdifferentialequations,JournalofComputationalandAppliedMathematics,2013,251:22-32.
随机热方程的渐近性分析
3.Foondun,Mohammud;Liu,Wei;Nane,Erkan;Somenon-existenceresultsforaclassofstochasticpartialdifferentialequations,JournalofDifferentialEquations,2019,266(5):2575-2596.
2.Liu,Wei;Tian,Kuanhou;Foondun,Mohammud;OnSomePropertiesofaClassofFractionalStochasticHeatEquations,JournalofTheoreticalProbability,2017,30:1310-1333.
1.Foondun,Mohammud;Liu,Wei;Omaba,McSylvester;Momentboundsforaclassoffractionalstochasticheatequations,AnnalsofProbability,2017,45(4):2131-2153.
随机控制
5.Qiu,Qinwei;Liu,Wei;Hu,Liangjian;Mao,Xuerong;You,Surong;StabilizationofstochasticdifferentialequationswithMarkovianswitchingbyfeedbackcontrolbasedondiscrete-timestateobservationwithatimedelay,Statistics&ProbabilityLetters,2016,115:16-26.
4.邱亲伟,刘暐,胡良剑,陆见秋,在离散观测和反馈延迟下的混杂随机系统镇定,控制理论与应用,2016,33(8):1023-1030.
3.Xu,Zhiying;Liu,Wei;Li,Yan;Hu,Junhao;Robustnessanalysisofglobalexponentialstabilityofnonlinearstochasticsystemswithrespecttoneutraltermsandtime-varyingdelays,AdvancesinDifferenceEquations,2015,105:1-14.
2.You,Surong;Liu,Wei;Lu,Jianqiu;Mao,Xuerong;Qiu,Qinwei;Stabilizationofhybridsystemsbyfeedbackcontrolbasedondiscrete-timestateobservationsd,SIAMJournalonControlandOptimization,2015,53(2):905-925.
1.Mao,Xuerong;LiuWei;Hu,Liangjian;Luo,Qi;Lu,Jianqiu;Stabilizationofhybridstochasticdifferentialequationsbyfeedbackcontrolbasedondiscrete-timestateobservations,Systems&ControlLetters,2014,73:88-95
学术兼职
ReviewerforMathematicalReviews
Reviewerforthefollowingjournals:
JournalofComputationalandAppliedMathematics
NumericalAlgorithms
AppliedMathematicsandComputation
AppliedNumericalMathematics
MediterraneanJournalofMathematics
DiscreteandContinuousDynamicalSystemsSeriesB
JournalofAppliedMathematicsandComputing
Stochastics:AnInternationalJournalofProbabilityandStochasticProcesses
SIAMJournalonControlandOptimization