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Ergodic theorems for higher order Cesàro means.
- Source :
-
Infinite Dimensional Analysis, Quantum Probability & Related Topics . Sep2023, Vol. 26 Issue 3, p1-20. 20p. - Publication Year :
- 2023
-
Abstract
- We investigate the convergence of higher order Cesàro means in Banach spaces. The main results of this paper are: (1) The proof of mean and Birkhoff-type ergodic theorems for higher order Cesàro means. (2) The existence of a one-to-one correspondence between convergent Cesàro means of different orders. (3) The proof of strong laws of large numbers for higher order sums of independent and identically distributed random elements. (4) A characterization of the ergodicity of measure preserving maps in terms of higher order mixing properties. To deal with higher order Cesàro means, one needs a notion of weighted mean more general than the one usually considered in the literature on weighted ergodic theorems. In this context, we also prove a characterization of generalized weighted means preserving Cesàro convergence. [ABSTRACT FROM AUTHOR]
- Subjects :
- *LAW of large numbers
*BANACH spaces
Subjects
Details
- Language :
- English
- ISSN :
- 02190257
- Volume :
- 26
- Issue :
- 3
- Database :
- Academic Search Index
- Journal :
- Infinite Dimensional Analysis, Quantum Probability & Related Topics
- Publication Type :
- Academic Journal
- Accession number :
- 172755454
- Full Text :
- https://doi.org/10.1142/S0219025722500151