Central Limit Theorem for Markov Chains with Variable Memory via the Chen-Stein Method

被引：0
作者：
Konane, Victorien [1 ,2 ]
Yameogo, Claude [2 ]
Baguian, Wahabo [2 ]
机构：
[1] Univ Joseph KI ZERBO, Math Dept, 03 BP 7021, Ouagadougou, Burkina Faso
[2] Lab Math & Informat, Ouagadougou, Burkina Faso
来源：
INTERNATIONAL JOURNAL OF ANALYSIS AND APPLICATIONS | 2025年 / 23卷
关键词：
Markov chains of variable length; persistent random walk; Chen-Stein method; counting process; risk model; RANDOM-WALK; APPROXIMATION; CONVERGENCE; ACCURACY;
D O I：
10.28924/2291-8639-23-2025-15
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
In this paper, we studied Markov chains of variable length and the convergence of persistent walk.We, also, looked at the rate of convergence of such process. We also provide the use of variable-memory stochastic chains in risk models.
引用
收藏
页数：16
相关论文
共 21 条
[1]  
[Anonymous], 1974, Rocky Mountain J. Math, DOI DOI 10.1216/RMJ-1974-4-3-497
[2]  
Barbour AD., 2005, An introduction to Steins method: lecture notes series, V4, DOI [10.1142/5792, DOI 10.1142/5792]
[3]   The accuracy of the Gaussian approximation to the sum of independent variates [J].
Berry, Andrew C. .
TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 1941, 49 (1-3) :122-136
[4]  
C‚nac P, 2012, Arxiv, DOI [arXiv:1208.3358, 10.48550/ARXIV.1208.3358, DOI 10.48550/ARXIV.1208.3358]
[5]  
Chen LHY, 2011, PROBAB APPL SER, P1, DOI 10.1007/978-3-642-15007-4
[6]   Chains of Infinite Order, Chains with Memory of Variable Length, and Maps of the Interval [J].
Collet, Pierre ;
Galves, Antonio .
JOURNAL OF STATISTICAL PHYSICS, 2012, 149 (01) :73-85
[7]  
Fernandez R, 2006, Arxiv, DOI [arXiv:math/0409539, 10.48550/ARXIV.MATH/0409539, DOI 10.48550/ARXIV.MATH/0409539]
[8]  
Gallo S, 2010, Arxiv, DOI [arXiv:1005.5459, 10.48550/ARXIV.1005.5459, DOI 10.48550/ARXIV.1005.5459]
[9]   ON DIFFUSION BY DISCONTINUOUS MOVEMENTS, AND ON THE TELEGRAPH EQUATION [J].
GOLDSTEIN, S .
QUARTERLY JOURNAL OF MECHANICS AND APPLIED MATHEMATICS, 1951, 4 (02) :129-156
[10]  
HARRIS TE, 1955, PAC J MATH, V5, P707, DOI DOI 10.2140/PJM.1955.5.707
123