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
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topLacey, 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
top- [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] A. Bellow, R.L. Jones and J. Rosenblatt, Almost everywhere convergence of weighted averages, Math. Ann., 293, 1992, p. 399-426. Zbl0736.28008MR1170516
- [3] V. Bergelson, M. Boshernitzan and J. Bourgain, Some results on non-linear recurrence, Preprint. Zbl0803.28011
- [4] N.H. Bingham and Ch. M. Goldie, Probabilistic and deterministic averaging, Trans. Amer. Math. Soc., 269, 1982, p. 453-480. Zbl0477.60032MR637702
- [5] J.R. Blum and R. Cogburn, On ergodic sequences of measures, Proc. Amer. Math. Soc., 51, 1975, p. 359-365. Zbl0309.43001MR372529
- [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] J. Bourgain, An approach to pointwise ergodic theorems, SpringerLecture Notes in Math., 1317, 1988, p. 204-223. Zbl0662.47006MR950982
- [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] A. Del Junco and J. Rosenblatt, Counterexamples in ergodic theory and number theory, Math. Ann., 245, 1979, p. 185-197. Zbl0398.28021MR553340
- [10] R. Durrett, Probability theory and examples, Wadsworth & Brooks/Cole, Belmont, CA, 1991, p. 394. Zbl0709.60002
- [11] P. Hall and C.C. Heyde, Martingale limit theory and its applications, Academic Press, New York, 1980. Zbl0462.60045MR624435
- [12] R. Jones, J. Olsen and M. Wierdl, Subsequence ergodic theorems for LP contractions, Trans. Amer. Math. Soc., To appear. Zbl0786.47005MR1043860
- [13] R. Jones and M. Wierdl, Examples of a.e. convergence and divergence of ergodic averages, Preprint. Zbl0828.28008MR1293406
- [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] K. Petersen, Ergodic Theory, Cambridge University Press, Cambridge and New York, 1983 and 1989. Zbl0507.28010MR833286
- [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] M. Wierdl, Pointwise ergodic theorem along the prime numbers, Israel J. Math., 64, 1988, p. 315-336. Zbl0695.28007MR995574
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- Michael T. Lacey, The return time theorem fails on infinite measure-preserving systems
- Dominique Schneider, Polynômes trigonométriques et marches aléatoires multidimensionnelles : application à la théorie ergodique
- Nadine Guillotin-Plantard, Clémentine Prieur, Central limit theorem for sampled sums of dependent random variables
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