Concentration inequalities and rates of convergence of the ergodic theorem for countable shifts with Gibbs measures

2021 ◽  
pp. 1-14
Author(s):  
Cesar Maldonado ◽  
Humberto Muñiz ◽  
Hugo Nieto Loredo
Keyword(s):  
Ergodic Theorem ◽  
Gibbs Measures ◽  
Rates Of Convergence ◽  
Concentration Inequalities

Exponential Rates of Convergence in the Ergodic Theorem: A Constructive Approach

2010 ◽  
Vol 139 (3) ◽  
pp. 367-374
Author(s):  
G. G. Bosco ◽  
F. P. Machado ◽  
Thomas Logan Ritchie
Keyword(s):  
Ergodic Theorem ◽  
Rates Of Convergence ◽  
Constructive Approach ◽  
Exponential Rates

Obtaining Prescribed Rates of Convergence for the Ergodic Theorem

1983 ◽  
Vol 35 (6) ◽  
pp. 1129-1146 ◽  
Author(s):  
G. L. O'Brien
Keyword(s):  
Ergodic Theorem ◽  
Law Of Large Numbers ◽  
Random Variables ◽  
Rates Of Convergence ◽  
Stationary Sequence ◽  
Strong Law ◽  
Iterated Logarithm ◽  
Large Numbers ◽  
The Law ◽  
Image Position

Let {Yn, n ∊ Z} be an ergodic strictly stationary sequence of random variables with mean zero, where Z denotes the set of integers. For n ∊ N = {1, 2, …}, let Sn = Y1 + Y2 + … + Yn. The ergodic theorem, alias the strong law of large numbers, says that n–lSn → 0 as n → ∞ a.s. If the Yn's are independent and have variance one, the law of the iterated logarithm tells us that this convergence takes place at the rate in the sense that1It is our purpose here to investigate what other rates of convergence are possible for the ergodic theorem, that is to say, what sequences {bn, n ≧ 1} have the property that2for some ergodic stationary sequence {Yn, n ∊ Z}.

Mean ergodic theorem in function symmetric spaces for infinite measure

2018 ◽  
Vol 2018 (1) ◽  
pp. 35-46
Author(s):  
Vladimir Chilin ◽  
◽  
Aleksandr Veksler ◽  
Keyword(s):  
Ergodic Theorem ◽  
Symmetric Spaces ◽  
Infinite Measure ◽  
Mean Ergodic Theorem
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