Ergodic theorems for extended real-valued random variables
We first establish a general version of the Birkhoff Ergodic Theorem for quasi-integrable extended real-valued random variables without assuming ergodicity. The key argument involves the Poincaré Recurrence Theorem. Our extension of the Birkhoff Ergodic Theorem is also shown to hold for asymptotic mean stationary sequences. This is formulated in terms of necessary and sufficient conditions. In particular, we examine the case where the probability space is endowed with a metric and we discuss the validity of the Birkhoff Ergodic Theorem for continuous random variables. The interest of our results is illustrated by an application to the convergence of statistical transforms, such as the moment generating function or the characteristic function, to their theoretical counterparts.
Year of publication: |
2010
|
---|---|
Authors: | Hess, Christian ; Seri, Raffaello ; Choirat, Christine |
Published in: |
Stochastic Processes and their Applications. - Elsevier, ISSN 0304-4149. - Vol. 120.2010, 10, p. 1908-1919
|
Publisher: |
Elsevier |
Keywords: | Birkhoff's Ergodic Theorem Asymptotic mean stationarity Extended real-valued random variables Non-integrable random variables Cesaro convergence Conditional expectation |
Saved in:
Online Resource
Saved in favorites
Similar items by person
-
The Analytic Hierarchy Process and the Theory of Measurement
Bernasconi, Michele, (2010)
-
Empirical properties of group preference aggregation methods employed in AHP: Theory and evidence
Bernasconi, Michele, (2014)
-
Bootstrap confidence sets for the Aumann mean of a random closed set
Choirat, Christine, (2014)
- More ...