用概率距离研究非时齐马氏链的收敛性

数学物理学报 ›› 2018, Vol. 38 ›› Issue (5): 963-969.

用概率距离研究非时齐马氏链的收敛性

朱志锋^1,²(),张绍义^1,*()

¹ 湖北大学数学与统计学学院武汉 430062
² 湖北工程学院数学与统计学院湖北孝感 432000

收稿日期:2017-04-23 出版日期:2018-11-09 发布日期:2018-11-09
通讯作者: 张绍义 E-mail:376574200@qq.com;zhshaoyi@aliyun.com
作者简介:朱志锋, E-mail:376574200@qq.com
基金资助:
湖北工程学院科研基金;(Z2014006)

Study on the Convergence of Nonhomogeneous Markov Chains with Probability Distance

Zhifeng Zhu^1,²(),Shaoyi Zhang^1,*()

¹ Mathematics and Statistics, Hubei University, Wuhan 430062
² Mathematics and Statistics, Hubei Engineering University, Hubei Xiaogan 432000

Received:2017-04-23 Online:2018-11-09 Published:2018-11-09
Contact: Shaoyi Zhang E-mail:376574200@qq.com;zhshaoyi@aliyun.com
Supported by:
the Hubei Engineering University Scientific Research Fund(Z2014006)

摘要/Abstract

摘要：

该文用概率距离和耦合方法研究了一般状态空间非时齐马氏链的收敛性，得到了一般状态空间非时齐马氏链收敛的一个条件.

关键词: 概率距离, 耦合方法, 非时齐马氏链, 收敛性

Abstract:

In this paper, we study the convergence of nonhomogeneous Markov chains in general state space by using the probability distance and the coupling property, a condition for convergence of nonhomogeneous Markov chains in general state space is obtained.

Key words: Probability distance, Coupling, Non homogeneous Markov chains, Convergence

中图分类号:

O211.4

朱志锋,张绍义. 用概率距离研究非时齐马氏链的收敛性[J]. 数学物理学报, 2018, 38(5): 963-969.

Zhifeng Zhu,Shaoyi Zhang. Study on the Convergence of Nonhomogeneous Markov Chains with Probability Distance[J]. Acta mathematica scientia,Series A, 2018, 38(5): 963-969.

参考文献 11

1	Chen M F . From Markov Chains to Nonequilibrium Particle Systems. SingaPore: World Scientific, 2004
2	Meyn S P , Tweedie R L . Markov Chains and Stochastic Stability. London: Springer-Verlag, 1992
3	Bowerman B , David H T , Isaacson D . The convergence of Cesaro averagesfor certain non-stationary Markov chains. Stachastic Processes and Their Applications, 1977, 5: 221- 230 doi: 10.1016/0304-4149(77)90032-1
4	龚光鲁, 钱敏平. 应用随机过程教程及在算法和智能计算中的随机模型. 北京: 清华大学出版社, 2004
	Gong Guanglu , Qian Minping . A Course in Appied Stochastic Processes and Stochastic Models in Algorithms and Intelligence Computation. Beijing: Tsinghua University Press, 2004
5	张绍义. 转移概率的可测耦合与概率距离. 数学年刊A辑, 1995, 6 (16): 769- 775
	Zhang Shaoyi . The measurable coupling and probability distance of transition probability. Chinese Annals of Mathematics, 1995, 6 (16): 769- 775
6	张绍义, 徐侃. 转移概率最优可测耦合的存在性. 数学学报, 1997, 1 (40): 5- 13
	Zhang Shaoyi , Xu Kan . The existence of optimal measurable coupling of transition probability. Acta Mathematica Sinica, 1997, 1 (40): 5- 13
7	Zhang S Y . Regularity and existence of invariant measures for jump processes. Acta Mathematica Sinica, 2005, 48: 785- 788
8	Zhang S Y . Existence of the optimal measurable coupling and ergodicity for markov processes. Science in China (Series A), 1999, 42: 58- 67 doi: 10.1007/BF02872050
9	Andradottir S . A method for discrete stochastic optimization. Management Science, 1995, 12 (41): 1946- 1961
10	Gutjahr W J , Pflug G C . Simulated annealing for noisy cost functions. Journal of Global Optimization, 1996, 8: 1- 13
11	Ahmed M A , Alkhamis T . M-Simulation-based optimization using simulated an. nealing with ranking and selection. Computers Operations Research, 2002, 29 (4): 387- 402 doi: 10.1016/S0305-0548(00)00073-3

[1]	杨轩, 阮小娥, 王彭. 时变切换信号驱动的线性连续切换系统的迭代学习控制收敛性分析[J]. 数学物理学报, 2018, 38(3): 599-612.
[2]	陈红斌, 甘四清, 徐大, 彭玉龙. 二维分数阶发展型方程的正式的二阶BDF交替方向隐式紧致差分格式[J]. 数学物理学报, 2017, 37(5): 976-992.
[3]	王学武. φ-半伪压缩算子对的Ishikawa型迭代程序的收敛性和稳定性[J]. 数学物理学报, 2017, 37(2): 248-256.
[4]	李炜. END序列加权和的完全收敛性[J]. 数学物理学报, 2016, 36(3): 448-455.
[5]	杨利琴, 邓方文. 非光滑有界凸域上全纯自映射的随机迭代[J]. 数学物理学报, 2015, 35(6): 1127-1135.
[6]	李英毅, 张海斌, 高欢. 一类修正邻近梯度法及其收敛性[J]. 数学物理学报, 2015, 35(6): 1136-1145.
[7]	李炜. NOD序列Sung型加权和的完全收敛性[J]. 数学物理学报, 2015, 35(4): 729-737.
[8]	赵杰. 椭圆重复齐次化问题W₀^1,p[J]. 数学物理学报, 2015, 35(3): 525-533.
[9]	万成高. 随机环境中马氏链函数加权和的极限定理[J]. 数学物理学报, 2015, 35(1): 163-171.
[10]	杨宇博, 祝鹏, 尹云辉. 奇异摄动问题最优阶一致收敛的间断有限元分析[J]. 数学物理学报, 2014, 34(3): 716-726.
[11]	陈加伟, 万仲平, 赵烈济. 可数族弱Bregman相对非扩展映像的收敛性分析[J]. 数学物理学报, 2014, 34(1): 70-79.
[12]	吴永锋. 两两NQD 列的L_p 收敛性和矩完全收敛性[J]. 数学物理学报, 2013, 33(5): 850-859.
[13]	胡慧英, 曾六川. 两个平衡问题和可数无穷多非扩张映像公共不动点问题的新的迭代算法[J]. 数学物理学报, 2013, 33(5): 860-881.
[14]	杨征, 纪园园, 马和平. Zakharov方程Fourier谱方法的一致收敛性[J]. 数学物理学报, 2013, 33(3): 409-423.
[15]	胡朝明, 万中, 王旭. 一种新的非单调谱共轭梯度算法[J]. 数学物理学报, 2013, 33(1): 78-88.