Hostname: page-component-586b7cd67f-dlnhk Total loading time: 0 Render date: 2024-11-20T08:28:12.327Z Has data issue: false hasContentIssue false
  • English
  • Français

Counting in Ergodic Theory

Published online by Cambridge University Press:  20 November 2018

Roger L. Jones ,
Joseph M. Rosenblatt  and
Máté Wierdl
Roger L. Jones
Affiliation:
Department of Mathematics, DePaul University, 2219 N. Kenmore, Chicago, Illinois 60614, U.S.A. email: [email protected]
Joseph M. Rosenblatt
Affiliation:
Department of Mathematics, University of Illinois at Urbana, Urbana, Illinois 61801, U.S.A. email: [email protected]
Máté Wierdl
Affiliation:
Department of Mathematical Sciences, University of Memphis, Memphis, Tennessee 38152, U.S.A. email: [email protected]
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

Many aspects of the behavior of averages in ergodic theory are a matter of counting the number of times a particular event occurs. This theme is pursued in this article where we consider large deviations, square functions, jump inequalities and related topics.

Keywords

****MISSING AMS CLASSIFICATION****
Type
Research Article
Information
Canadian Journal of Mathematics , Volume 51 , Issue 5 , 01 October 1999 , pp. 996 - 1019
Copyright
Copyright © Canadian Mathematical Society 1999

References

[1] Akcoglu, M., Jones, R. L. and Rosenblatt, J., The worst sums in ergodic theory. (preprint).Google Scholar
[2] Assani, I., Strong laws for weighted sums of independent identically distributed random variables. Duke Math. J. (2) 88(1997), 217–246.Google Scholar
[3] Assani, I., Convergence of the p-series for stationary sequences. New York Journal of Math. 3A(1997), 15–30, in the Proceedings of the New York Journal of Mathematics Conference, June 9–13, 1997.Google Scholar
[4] Bishop, E., An upcrossing inequality with applications. Michigan Math. J. 13(1966), 1–13.Google Scholar
[5] Bishop, E., Foundations of Constructive Analysis. McGraw-Hill, 1967.Google Scholar
[6] Bourgain, J., Pointwise ergodic theorems for arithmetic sets. Inst. Hautes Études Sci. Publ. Math. 69(1989), 5–45.Google Scholar
[7] Burkholder, D. and Gundy, R., Extrapolation and interpolation of quasi-linear operators on martingales. Acta Math. 124(1970), 249–304.Google Scholar
[8] Doob, J., Stochastic Processes. JohnWiley & Sons, Inc., New York, Chapman & Hall, Limited, London, 1953.Google Scholar
[9] Garsia, A., Topics in Almost Everywhere Convergence. Lectures in AdvancedMathematics,Markham Publishing, Chicago, 1970.Google Scholar
[10] Ivanov, V. V., Geometric properties of monotone functions and probabilities of random fluctuations. Siberian Math. J. (1) 37(1996), 102–129.Google Scholar
[11] Jones, R. L., Inequalities for the ergodic maximal function. StudiaMath. 40(1977), 111–129.Google Scholar
[12] Jones, R. L., Ostrovskii, I. and Rosenblatt, J., Square functions in ergodic theory. Ergodic Theory Dynamical Systems 16(1996), 267–305.Google Scholar
[13] Jones, R. L., Kaufman, R., Rosenblatt, J., and Wierdl, M., Oscillation in ergodic theory. Ergodic Theory Dynamical Systems 18(1998), 889–935.Google Scholar
[14] Kachurovskii, A. G., The rate of convergence in ergodic theorems. Russian Math. Surveys (4) 51(1996), 653–703.Google Scholar
[15] Kalikow, S. and Weiss, B., Fluctuations of ergodic averages. (preprint).Google Scholar
[16] Rosenblatt, J. and Wierdl, M., Fourier Analysis and Almost Everywhere Convergence. Proceedings of the Conference on Ergodic Theory and its Connections with Harmonic Analysis, Alexandria, Egypt, Cambridge University Press, 1994, 3–151.Google Scholar