PL EN


Preferencje help
Widoczny [Schowaj] Abstrakt
Liczba wyników
2000 | 84/85 | 2 | 457-480
Tytuł artykułu

Marches en milieu aléatoire et mesures quasi-invariantes pour un système dynamique

Treść / Zawartość
Warianty tytułu
Języki publikacji
FR EN
Abstrakty
EN
The invariant measures for a Markovian operator corresponding to a random walk, in a random stationary one-dimensional environment defined by a dynamical system, are quasi-invariant measures for the system. We discuss the construction of such measures in the general case and show unicity, under some assumptions, for a rotation on the circle.
Słowa kluczowe
Rocznik
Tom
Numer
2
Strony
457-480
Opis fizyczny
Daty
wydano
2000
otrzymano
1999-09-02
poprawiono
2000-01-06
Twórcy
  • IRMAR, Université de Rennes I, Campus de Beaulieu, 35042 Rennes Cedex, France
  • IRMAR, Université de Rennes I, Campus de Beaulieu, 35042 Rennes Cedex, France
Bibliografia
  • [1] S. Alili, Processus de branchement et marche aléatoire en milieux désordonnés, thèse, Université Pierre et Marie Curie (Paris VI), 1993.
  • [2] D. Anosov, On the additive functional homological equation associated with an irrational rotation of the circle, Izv. Akad. Nauk SSSR 37 (1973), 1259-1274 (in Russian).
  • [3] R. Bowen, Equilibrium States and the Ergodic Theory of Anosov Diffeomorphisms, Lecture Notes in Math. 470, Springer, 1975.
  • [4] J. Brémont, Comportement des sommes ergodiques pour des rotations et des fonctions continues peu régulières, Publications des Séminaires de Rennes, 1999.
  • [5] J.-P. Conze, Equirépartition et ergodicité de transformations cylindriques, Publications des Séminaires de Rennes, 1976.
  • [6] J.-P. Conze et Y. Guivarc'h, Croissance des sommes ergodiques et principe va- riationnel, preprint, Rennes, 1997.
  • [7] M. Denker, C. Grillenberger and K. Sigmund, Ergodic Theory on Compact Spaces, Lecture Notes in Math. 527, Springer, 1976.
  • [8] H. Federer, Geometric Measure Theory, Classics in Math., Springer, 1996.
  • [9] Y. Guivarc'h et J. Hardy, Théorèmes limites pour une classe de chaînes de Markov et applications aux difféomorphismes d'Anosov, Ann. Inst. H. Poincaré Sér. Probab. Statist. 24 (1988), 73-98.
  • [10] G. Halász, Remarks on the remainder in Birkhoff's ergodic theorem, Acta Math. Acad. Sci. Hungar. 28 (1976), 389-395.
  • [11] M. R. Herman, Sur la conjugaison différentiable des difféomorphismes du cercle à des rotations, Publ. Math. Inst. Hautes Etudes Sci. 49 (1979), 5-233.
  • [12] H. Kesten, M. V. Kozlov and F. Spitzer, A limit law for random walks in a random environment, Compositio Math. 30 (1975), 145-168.
  • [13] S. M. Kozlov, The method of averaging and walks in inhomogeneous environments, Russian Math. Surveys 40 (1985), no. 2, 73-145.
  • [14] S. M. Kozlov and S. A. Molchanov, On conditions for applicability of the central limit theorem to random walks on a lattice, Soviet Math. Dokl. 30 (1984), 410-413.
  • [15] M. A. Krasnosel'skiĭ, Positive Solutions of Operator Equations, Noordhoff, Gro- ningen, 1964.
  • [16] U. Krengel, Ergodic Theorems, de Gruyter, Berlin, 1985.
  • [17] A. V. Letchikov, A criterion for applicability of the CLT to one-dimensional random walks in random environments, Theory Probab. Appl. 37 (1992), 553-557.
  • [18] W. de Melo and S. van Strien, One-Dimensional Dynamics, Ergeb. Math. Grenzgeb. 25, Springer, 1993.
  • [19] S. A. Molchanov, Lectures on random media, in: Lectures on Probability Theory (Saint-Flour, 1992), Lecture Notes in Math. 1581, Springer, 1994, 242-411.
  • [20] M. F. Norman, Markov Processes and Learning Models, Academic Press, New York, 1972.
  • [21] Y. Peres, A combinatorial application of the maximal ergodic theorem, Bull. London Math. Soc. 20 (1988), 248-252.
  • [22] Ya. G. Sinai, Construction of Markov partitions, Funktsional. Anal. i Prilozhen. 2 (1968), no. 3, 70-80 (in Russian).
  • [23] Ya. G. Sinai, The limiting behaviour of a one-dimensional random walk in a random environment, Theory Probab. Appl. 27 (1982), 256-268.
  • [24] Ya. G. Sinai, Simple random walks on tori, preprint.
  • [25] R. Sine, On invariant probabilities for random rotations, Israel J. Math. 33 (1979), 384-388.
  • [26] F. Solomon, Random walks in a random environment, Ann. Probab. 3 (1975), 1-31.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.bwnjournal-article-cmv84i2p457bwm
JavaScript jest wyłączony w Twojej przeglądarce internetowej. Włącz go, a następnie odśwież stronę, aby móc w pełni z niej korzystać.