Coupling, spectral gap and related topics (Ⅰ) 被引量：1

Coupling, spectral gap and related topics (Ⅰ)

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摘要 THIS is the first of a series of three reviews. They are partially surveys on three aspects: (ⅰ) explaining the main ideas of our recent application of the coupling method to the estimation of spectral gap, (ⅱ) introducing some more recent progress on the study on some related topics,(ⅲ) collecting some open problems for the further study.

作者 CHEN MufaDepartment of Mathematics, Beijing Normal University, Beijing 100875, China

出处《Chinese Science Bulletin》 SCIE EI CAS 1997年第16期1321-1327,共7页

关键词 DIFFUSIONS MANIFOLD MARKOV CHAINS spectral gap couplings. diffusions, manifold, Markov chains, spectral gap, couplings.

分类号 O211.6 [理学—概率论与数理统计]

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相关文献

参考文献28

1王凤雨,徐美萍.关于多维扩散过程耦合的保序性(英文)[J].应用概率统计,1997,13(2):142-148. 被引量：2
2张绍义,徐侃.转移概率最优可测耦合的存在性[J].数学学报（中文版）,1997,40(1):5-13. 被引量：9
3陈木法,王凤雨.Application of Coupling Method to the First Eigenvalue on Manifold[J].Science China Mathematics,1994,37(1):1-14. 被引量：4
4Chen Mufa Department of Mathematics Beijing Normal University Beijing, 100875 China.Estimation of Spectral Gap for Markov Chains[J].Acta Mathematica Sinica,English Series,1996,12(4):337-360. 被引量：14
5Hermann Thorisson.Shift-coupling in continuous time[J]. Probability Theory and Related Fields . 1994 (4)
6Chen Mufa Department of Mathematics Beijing Normal University Beijing,100875 China.Optimal Markovian Couplings and Applications[J].Acta Mathematica Sinica,English Series,1994,10(3):260-275. 被引量：6
7Mu -Fa Chen.Ergodic theorems for reaction-diffusion processes[J]. Journal of Statistical Physics . 1990 (5-6)
8Chen,M. F.Ergodic theorems for reaction-diffusion processes, J.Star. Physica . 1990
9Y. H. Zhang.Conservativity of couplings for jump processes (in Chinese). Journal of Beijing Normal University Natural Science . 1994
10Lindvall T,Rogers L C G.Coupling of multidimensional diffusion processes. The Annals of Probability . 1986

二级参考文献8

1陈木法，Technical Report Series of the Laboratory for Research inStatistics and Probability，1993年
2陈木法，World Sci，1992年
3吴智泉，巴氏空间上的概率论，1990年
4王金德，随机线性规划（译），1988年
5陈家鼎，应用数学学报，1983年，3期，367页
6Chen M F，Acta Math Sin New Ser，1994年，10卷，260页
7Chen M F，Probab Theor Relat Fields，1993年，95卷，421页
8Chen M F，Ann Probab，1989年，17卷，151页

共引文献28

1陈木法.Variational formulas and approximation theorems for the first eigenvalue in dimension one[J].Science China Mathematics,2001,44(4):409-418. 被引量：16
2陈木法.Analytic proof of dual variational formula for the first eigenvalue in dimension one[J].Science China Mathematics,1999,42(8):805-815. 被引量：27
3王颖喆.R^n上扩散过程的代数式收敛[J].数学学报（中文版）,2004,47(5):1001-1012. 被引量：2
4周玉兰,毛永华.有界马氏算子的泛函不等式与本质谱的问题[J].北京师范大学学报（自然科学版）,2006,42(3):229-231.
5邵井海,毛永华.树上生灭过程的Dirichlet特征值估计[J].数学学报（中文版）,2007,50(3):507-516. 被引量：1
6张丽华,张余辉.Latala-Oleszkiewicz不等式的常数估计[J].数学进展,2007,36(6):672-678.
7张绍义.跳过程ρ最优耦合算子的存在性[J].数学学报（中文版）,1998,41(2):393-398. 被引量：5
8张绍义.最优可测耦合的存在性与Markov过程的遍历性[J].中国科学（A辑）,1998,28(11):999-1008. 被引量：8
9张绍义.关于ρ最优可测耦合若干应用的注记[J].科学通报,1999,44(3):265-268.
10徐立峰,严慧,徐侃.一类随机系统平稳分布的存在性与唯一性[J].数学杂志,2010,30(4):712-720. 被引量：1

同被引文献5

1陈木法.Analytic proof of dual variational formula for the first eigenvalue in dimension one[J].Science China Mathematics,1999,42(8):805-815. 被引量：27
2陈木法,王凤雨.General formula for lower bound of the first eigenvalue on Riemannian manifolds[J].Science China Mathematics,1997,40(4):384-394. 被引量：10
3陈木法.Explicit bounds of the first eigenvalue[J].Science China Mathematics,2000,43(10):1051-1059. 被引量：27
4Chen Mufa Department of Mathematics Beijing Normal University Beijing, 100875 China.Estimation of Spectral Gap for Markov Chains[J].Acta Mathematica Sinica,English Series,1996,12(4):337-360. 被引量：14
5Chen Mufa Department of Mathematics, Beijing Normal University, Beijing 100875, China.Estimate of Exponential Convergence Rate in Total Variation by Spectral Gap[J].Acta Mathematica Sinica,English Series,1998,14(1):9-16. 被引量：4

引证文献1

1陈木法.Variational formulas and approximation theorems for the first eigenvalue in dimension one[J].Science China Mathematics,2001,44(4):409-418. 被引量：16

二级引证文献16

1ZHANG MeiRong 1,2 1 Department of Mathematical Sciences,Tsinghua University,Beijing 100084,China,2 Zhou Pei-Yuan Center for Applied Mathematics,Tsinghua University,Beijing 100084,China.Extremal eigenvalues of measure differential equations with fixed variation[J].Science China Mathematics,2010,53(10):2573-2588. 被引量：3
2ZHANG MeiRong Department of Mathematical Sciences,Zhou Pei-Yuan Center for Applied Mathematics,Tsinghua University,Beijing 100084,China.Continuity in weak topology:higher order linear systems of ODE[J].Science China Mathematics,2008,51(6):1036-1058. 被引量：3
3陈木法.直线上函数的Banach空间的Poincaré型不等式的变分公式[J].数学学报（中文版）,2005,48(2):209-220. 被引量：2
4Mu Fa CHEN.Spectral Gap and Logarithmic Sobolev Constant for Continuous Spin Systems[J].Acta Mathematica Sinica,English Series,2008,24(5):705-736. 被引量：4
5章梅荣.高阶线性常微分方程组在弱拓扑下的连续性[J].中国科学（A辑）,2008,38(4):398-417.
6章梅荣.测度微分方程在固定变差时的极端特征值谨以此文致《中国科学》创刊六十周年[J].中国科学：数学,2010,40(12):1137-1152.
7刘伟,彭高辉.关于生灭过程的Cheeger型等周不等式(英文)[J].数学杂志,2011,31(4):653-658.
8靳荷艳,毛永华.半直线上L^p-Poincaré不等式最优常数的估计[J].数学学报（中文版）,2012,55(1):169-178. 被引量：1
9Mu-Fa CHEN Lingdi WANG Yuhui ZHANG.Mixed principal eigenvalues in dimension one[J].Frontiers of Mathematics in China,2013,8(2):317-343. 被引量：4
10Yutao MA Yonghua MAO.New point view of spectral gap in functional spaces for birth-death processes[J].Frontiers of Mathematics in China,2014,9(3):523-535.

1CHEN Muf aDepartment of Mathematics, Beijing Normal University, Beijing 100875, China.Coupling, spectral gap and related topics (Ⅱ)[J].Chinese Science Bulletin,1997,42(17):1409-1416. 被引量：2
2CHEN MufaDepartment of Mathematics, Beijing Normal University, Beijing 100875, China.Coupling, spectral gap and related topics (Ⅲ)[J].Chinese Science Bulletin,1997,42(18):1497-1505. 被引量：2
3Yong Hua MAO,Yan Hong SONG.Spectral Gap and Convergence Rate for Discrete-time Markov Chains[J].Acta Mathematica Sinica,English Series,2013,29(10):1949-1962. 被引量：3
4原存德,裴永珍.PERSISTENCE OF TWO-SPECIES AYALA COMPETITIVE MODEL WITH DIFFERENT DIFFUSIONS[J].Applied Mathematics and Mechanics(English Edition),1999,20(4):118-125.
5何银年,李开泰.STOKES COUPLING METHOD FOR THE EXTERIOR FLOW PART Ⅰ:APPROXIMATE ACCURACY[J].Acta Mathematicae Applicatae Sinica,1999,15(3):333-336.
6赵慧明,董正筑,曹璎珞.THE COUPLING METHOD FOR TORSION PROBLEM OF THE SQUARE CROSS-SECTION BAR WITH CRACKS[J].Applied Mathematics and Mechanics(English Edition),2000,21(11):1308-1313.
7丁灯.A NOTE ON STOCHASTIC OPTIMAL CONTROL OF REFLECTED DIFFUSIONS WITH JUMPS[J].Applied Mathematics and Mechanics(English Edition),2000,21(9):1079-1090.
8Alberto CAVICCHIOLI(Department Of Mathematics,University of Modena,Via Campi 213/B, 41100 Modena, Italy,)Dusan REPOVS(Institute for Mathematics, Physics and Mechanics,University of Ljubljana,P. O. Box 64, Ljubljana 61111,Slovenia.Some Open Problems in Geometric Topologyof Low Dimensions[J].Chinese Quarterly Journal of Mathematics,1995,10(4):8-14.
9Xing FANG,Ping HE,Jiangang YING.Dirichlet Forms Associated with Linear Diffusions[J].Chinese Annals of Mathematics,Series B,2010,31(4):507-518. 被引量：2
10CHEN MufaDepartment of Mathematics, Beijing Normal University, Beijing 100875, China.Eigenvalues, inequalities and ergodic theory[J].Chinese Science Bulletin,2000,45(9):769-774. 被引量：7

Chinese Science Bulletin

1997年第16期

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