Large deviations for generic stationary processes

Emmanuel Lesigne; Dalibor Volný

Colloquium Mathematicae (2000)

  • Volume: 84/85, Issue: 1, page 75-82
  • ISSN: 0010-1354

Abstract

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Let (Ω,A,μ,T) be a measure preserving dynamical system. The speed of convergence in probability in the ergodic theorem for a generic function on Ω is arbitrarily slow.

How to cite

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Lesigne, Emmanuel, and Volný, Dalibor. "Large deviations for generic stationary processes." Colloquium Mathematicae 84/85.1 (2000): 75-82. <http://eudml.org/doc/210810>.

@article{Lesigne2000,
abstract = {Let (Ω,A,μ,T) be a measure preserving dynamical system. The speed of convergence in probability in the ergodic theorem for a generic function on Ω is arbitrarily slow.},
author = {Lesigne, Emmanuel, Volný, Dalibor},
journal = {Colloquium Mathematicae},
keywords = {ergodic theorem; probability space; measure-preserving ergodic and aperiodic transformation; speed of convergence},
language = {eng},
number = {1},
pages = {75-82},
title = {Large deviations for generic stationary processes},
url = {http://eudml.org/doc/210810},
volume = {84/85},
year = {2000},
}

TY - JOUR
AU - Lesigne, Emmanuel
AU - Volný, Dalibor
TI - Large deviations for generic stationary processes
JO - Colloquium Mathematicae
PY - 2000
VL - 84/85
IS - 1
SP - 75
EP - 82
AB - Let (Ω,A,μ,T) be a measure preserving dynamical system. The speed of convergence in probability in the ergodic theorem for a generic function on Ω is arbitrarily slow.
LA - eng
KW - ergodic theorem; probability space; measure-preserving ergodic and aperiodic transformation; speed of convergence
UR - http://eudml.org/doc/210810
ER -

References

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  1. [Bu-Den] Burton, R. and Denker, M. On the central limit theorem for dynamical systems, Trans. Amer. Math. Soc. 302 (1987), 715-726. Zbl0628.60030
  2. [C] Cramér, H. Sur un nouveau théorème-limite de la théorie des probabilités, in: Actualités Sci. Indust. 736, Hermann, Paris, 1938, 5-23. Zbl64.0529.01
  3. s Dembo, A. and Zeitouni, O. Large Deviations Techniques and Applications, Jones and Bartlett, Boston, 1993 (or: Appl. Math. 38, Springer, 1998). Zbl0793.60030
  4. s del Junco, A. and Rosenblatt, J. Counterexamples in ergodic theory and in number theory, Math. Ann. 245 (1979), 185-197. Zbl0398.28021
  5. [K] Katok, A. Constructions in ergodic theory, unpublished manuscript. Zbl1030.37001
  6. [Kr] Krengel, U. On the speed of convergence in the ergodic theorem, Monatsh. Math. 86 (1978), 3-6. Zbl0352.28008
  7. [L1] Lacey, M. On weak convergence in dynamical systems to self-similar processes with spectral representation, Trans. Amer. Math. Soc. 328 (1991), 767-778. Zbl0741.60026
  8. [L2] Lacey, M. On central limit theorems, modulus of continuity and Diophantine type for irrational rotations, J. Anal. Math. 61 (1993), 47-59. 
  9. [Pa] Parry, W. Topics in Ergodic Theory, Cambridge Univ. Press, 1981. Zbl0449.28016
  10. [Pe] Petrov, V. V. Limit Theorems of Probability Theory, Oxford Stud. Probab. 4, Oxford Sci. Publ., Oxford Univ. Press, 1995. 
  11. [V1] Volný, D. On limit theorems and category for dynamical systems, Yokohama Math. J. 38 (1990), 29-35. Zbl0735.60025
  12. [V2] Volný, D, Invariance principles and Gaussian approximation for strictly stationary processes, Trans. Amer. Math. Soc. 351 (1999), 3351-3371. Zbl0939.37006
  13. [V-W] Volný, D. and Weiss, B. Coboundaries in L 0 ∞ , in preparation. Zbl1055.60018

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