Random ergodic theorems with universally representative sequences

Michael Lacey; Karl Petersen; Mate Wierdl; Dan Rudolph

Annales de l'I.H.P. Probabilités et statistiques (1994)

  • Volume: 30, Issue: 3, page 353-395
  • ISSN: 0246-0203

How to cite

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Lacey, Michael, et al. "Random ergodic theorems with universally representative sequences." Annales de l'I.H.P. Probabilités et statistiques 30.3 (1994): 353-395. <http://eudml.org/doc/77487>.

@article{Lacey1994,
author = {Lacey, Michael, Petersen, Karl, Wierdl, Mate, Rudolph, Dan},
journal = {Annales de l'I.H.P. Probabilités et statistiques},
keywords = {measure preserving transformations; shift invariant measure; random ergodic theorems; coin tossing measure; return time theorem},
language = {eng},
number = {3},
pages = {353-395},
publisher = {Gauthier-Villars},
title = {Random ergodic theorems with universally representative sequences},
url = {http://eudml.org/doc/77487},
volume = {30},
year = {1994},
}

TY - JOUR
AU - Lacey, Michael
AU - Petersen, Karl
AU - Wierdl, Mate
AU - Rudolph, Dan
TI - Random ergodic theorems with universally representative sequences
JO - Annales de l'I.H.P. Probabilités et statistiques
PY - 1994
PB - Gauthier-Villars
VL - 30
IS - 3
SP - 353
EP - 395
LA - eng
KW - measure preserving transformations; shift invariant measure; random ergodic theorems; coin tossing measure; return time theorem
UR - http://eudml.org/doc/77487
ER -

References

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  1. [1] A. Bellow and V. Losert, The weighted pointwise ergodic theorem and the individual ergodic theorem along subsequences, Trans. Amer. Math. Soc., 288, 1985, p. 307-345. Zbl0619.47004MR773063
  2. [2] A. Bellow, R.L. Jones and J. Rosenblatt, Almost everywhere convergence of weighted averages, Math. Ann., 293, 1992, p. 399-426. Zbl0736.28008MR1170516
  3. [3] V. Bergelson, M. Boshernitzan and J. Bourgain, Some results on non-linear recurrence, Preprint. Zbl0803.28011
  4. [4] N.H. Bingham and Ch. M. Goldie, Probabilistic and deterministic averaging, Trans. Amer. Math. Soc., 269, 1982, p. 453-480. Zbl0477.60032MR637702
  5. [5] J.R. Blum and R. Cogburn, On ergodic sequences of measures, Proc. Amer. Math. Soc., 51, 1975, p. 359-365. Zbl0309.43001MR372529
  6. [6] J. Bourgain, On the maximal ergodic theorem for certain substets of the integers, Israel J. Math., 61, 1988, p. 39-72. Zbl0642.28010MR937581
  7. [7] J. Bourgain, An approach to pointwise ergodic theorems, SpringerLecture Notes in Math., 1317, 1988, p. 204-223. Zbl0662.47006MR950982
  8. [8] J. Bourgain, H. Furstenberg, Y. Katznelson and D. Ornstein, Return times of dynamical systems, appendix to Pointwise ergodic theorems for arithmetic sets, by J. Bourgain, Pub. Math. I.H.E.S., 69, 1989, p. 5-45. Zbl0705.28008MR1019960
  9. [9] A. Del Junco and J. Rosenblatt, Counterexamples in ergodic theory and number theory, Math. Ann., 245, 1979, p. 185-197. Zbl0398.28021MR553340
  10. [10] R. Durrett, Probability theory and examples, Wadsworth & Brooks/Cole, Belmont, CA, 1991, p. 394. Zbl0709.60002
  11. [11] P. Hall and C.C. Heyde, Martingale limit theory and its applications, Academic Press, New York, 1980. Zbl0462.60045MR624435
  12. [12] R. Jones, J. Olsen and M. Wierdl, Subsequence ergodic theorems for LP contractions, Trans. Amer. Math. Soc., To appear. Zbl0786.47005MR1043860
  13. [13] R. Jones and M. Wierdl, Examples of a.e. convergence and divergence of ergodic averages, Preprint. Zbl0828.28008MR1293406
  14. [14] L. Meilijson, The average of the value of a function at random points, Israel J. Math., 15, 1973, p. 193-203. Zbl0275.60069MR329010
  15. [15] K. Petersen, Ergodic Theory, Cambridge University Press, Cambridge and New York, 1983 and 1989. Zbl0507.28010MR833286
  16. [16] K. Petersen, On a series of cosecants related to a problem in ergodic theory, Comp. Math., 26, 1973, p. 313-317. Zbl0269.10030MR325927
  17. [17] M. Wierdl, Pointwise ergodic theorem along the prime numbers, Israel J. Math., 64, 1988, p. 315-336. Zbl0695.28007MR995574

Citations in EuDML Documents

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  1. Catherine Gamet, Dominique Schneider, Théorèmes ergodiques multidimensionnels et suites aléatoires universellement représentatives en moyenne
  2. Nadine Guillotin-Plantard, Sur la convergence faible des systèmes dynamiques échantillonnés
  3. Michael T. Lacey, The return time theorem fails on infinite measure-preserving systems
  4. Dominique Schneider, Polynômes trigonométriques et marches aléatoires multidimensionnelles : application à la théorie ergodique
  5. Nadine Guillotin-Plantard, Clémentine Prieur, Central limit theorem for sampled sums of dependent random variables

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