ERGODIC PROPERTIES OF MARKOV MAPS IN RD

被引：5
|
作者：
BUGIEL, P
机构：
[1] Department of Mathematics, Jagellonian University, Kraków, PL-30-059
来源：
PROBABILITY THEORY AND RELATED FIELDS | 1991年 / 88卷 / 04期
关键词：
D O I：
10.1007/BF01192553
中图分类号：
O21 [概率论与数理统计]; C8 [统计学];
学科分类号：
020208 ; 070103 ; 0714 ;
摘要：
For domains I subset-of R(d) (bounded or not) the notion of a Markov map from I into itself is developed. It is shown that under a condition of Renyi type and the assumption that the map phi is Markov, any probability density tends in L1-norm to a unique invariant measure under the action of the Perron-Frobenius operator P-phi. The smoothness and ergodic properties of that invariant measure are studied. The paper generalizes results of Lasota and Yorke from dimension one to higher dimension.
引用
收藏
页码：483 / 496
页数：14
相关论文
共 50 条
  • [1] ENTROPY VERSUS SPEED IN ERGODIC MARKOV MAPS
    FRIEDMAN, N
    BOYARSKY, A
    SIAM JOURNAL ON ALGEBRAIC AND DISCRETE METHODS, 1984, 5 (01): : 82 - 93
  • [2] Ergodic properties of Markov processes
    Rey-Bellet, Luc
    OPEN QUANTUM SYSTEMS II: THE MARKOVIAN APPROACH, 2006, 1881 : 1 - 39
  • [3] Ergodic properties for Markov chains
    不详
    LIMIT THEOREMS FOR MARKOV CHAINS AND STOCHASTIC PROPERTIES OF DYNAMICAL SYSTEMS BY QUASI-COMPACTNESS, 2001, 1766 : 60 - 62
  • [4] An exceptional set in the ergodic theory of Markov maps of the interval
    Abercrombie, AG
    Nair, R
    PROCEEDINGS OF THE LONDON MATHEMATICAL SOCIETY, 1997, 75 : 221 - 240
  • [5] ERGODIC PROPERTIES OF CONDITIONAL MARKOV CHAINS
    BEZHAEVA, ZI
    DOKLADY AKADEMII NAUK SSSR, 1973, 211 (04): : 761 - 763
  • [6] A COUNTER EXAMPLE IN THE ERGODIC THEORY OF EXPANDING MARKOV MAPS OF THE INTERVAL
    Abercrombie, A. G.
    Nair, R.
    MATHEMATICAL RESEARCH LETTERS, 1994, 1 (06) : 765 - 768
  • [7] Ergodic properties of fibered rational maps
    Jonsson, M
    ARKIV FOR MATEMATIK, 2000, 38 (02): : 281 - 317
  • [8] ERGODIC PROPERTIES OF FOLDING MAPS ON SPHERES
    Burchard, Almut
    Chambers, Gregory R.
    Dranovski, Anne
    DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS, 2017, 37 (03) : 1183 - 1200
  • [9] SOME ERGODIC PROPERTIES OF RATIONAL MAPS
    LEDRAPPIER, F
    COMPTES RENDUS DE L ACADEMIE DES SCIENCES SERIE I-MATHEMATIQUE, 1984, 299 (01): : 37 - 40
  • [10] Ergodic properties of bimodal circle maps
    Crovisier, Sylvain
    Guarino, Pablo
    Palmisano, Liviana
    ERGODIC THEORY AND DYNAMICAL SYSTEMS, 2019, 39 : 1462 - 1500
12345