LU-Factorization Versus Wiener-Hopf Factorization for Markov Chains

被引：0
|
作者：
Vincent Vigon
机构：
[1] Université de Strasbourg,IRMA
来源：
Acta Applicandae Mathematicae | 2013年 / 128卷
关键词：
Markov chains; Random walks; LU-factorization; Path-decomposition; Fluctuation theory; Probabilistic potential theory; Infinite matrices; 60J10; 60J45; 47A68; 15A23;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
Our initial motivation was to understand links between Wiener-Hopf factorizations for random walks and LU-factorizations for Markov chains as interpreted by Grassman (Eur. J. Oper. Res. 31(1):132–139, 1987). Actually, the first ones are particular cases of the second ones, up to Fourier transforms. To show this, we produce a new proof of LU-factorizations which is valid for any Markov chain with a denumerable state space equipped with a pre-order relation. Factors have nice interpretations in terms of subordinated Markov chains. In particular, the LU-factorization of the potential matrix determines the law of the global minimum of the Markov chain.
引用
收藏
页码：1 / 37
页数：36
相关论文
共 50 条
  • [1] LU-Factorization Versus Wiener-Hopf Factorization for Markov Chains
    Vigon, Vincent
    ACTA APPLICANDAE MATHEMATICAE, 2013, 128 (01) : 1 - 37
  • [2] Wiener-Hopf factorization technique for time-inhomogeneous finite Markov chains
    Bielecki, Tomasz R.
    Cheng, Ziteng
    Cialenco, Igor
    Gong, Ruoting
    STOCHASTICS-AN INTERNATIONAL JOURNAL OF PROBABILITY AND STOCHASTIC PROCESSES, 2021, 93 (01) : 130 - 166
  • [3] WIENER-HOPF FACTORIZATION FOR TIME-INHOMOGENEOUS MARKOV CHAINS AND ITS APPLICATION
    Bielecki, Tomasz R.
    Cialenco, Igor
    Gong, Ruoting
    Huang, Yicong
    PROBABILITY AND MATHEMATICAL STATISTICS-POLAND, 2020, 40 (02): : 225 - 244
  • [4] A Note on Wiener-Hopf Factorization for Markov Additive Processes
    Klusik, Przemysaw
    Palmowski, Zbigniew
    JOURNAL OF THEORETICAL PROBABILITY, 2014, 27 (01) : 202 - 219
  • [5] ON THE SYMMETRIC WIENER-HOPF FACTORIZATION FOR MARKOV ADDITIVE PROCESSES
    KASPI, H
    ZEITSCHRIFT FUR WAHRSCHEINLICHKEITSTHEORIE UND VERWANDTE GEBIETE, 1982, 59 (02): : 179 - 196
  • [6] FACTORIZATION OF A WIENER-HOPF MATRIX
    JONES, DS
    IMA JOURNAL OF APPLIED MATHEMATICS, 1984, 32 (1-3) : 211 - 220
  • [7] MATRIX WIENER-HOPF FACTORIZATION
    RAWLINS, AD
    WILLIAMS, WE
    QUARTERLY JOURNAL OF MECHANICS AND APPLIED MATHEMATICS, 1981, 34 (FEB): : 1 - 8
  • [8] On the Wiener-Hopf type factorization of an operator
    Sunyach, C
    COMPTES RENDUS DE L ACADEMIE DES SCIENCES SERIE I-MATHEMATIQUE, 1999, 329 (05): : 405 - 408
  • [9] Asymptotic factorization of Wiener-Hopf kernels
    Crighton, DG
    WAVE MOTION, 2001, 33 (01) : 51 - 65
  • [10] Weyl metrics and Wiener-Hopf factorization
    Aniceto, P.
    Camara, M. C.
    Cardoso, G. L.
    Rossello, M.
    JOURNAL OF HIGH ENERGY PHYSICS, 2020, 2020 (05)
12345