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2013 On the Dependence of the Limit Functions on the Random Parameters in Random Ergodic Theorems
Takeshi Yoshimoto
Abstr. Appl. Anal. 2013(SI59): 1-13 (2013). DOI: 10.1155/2013/503689

Abstract

We study the structure of the ergodic limit functions determined in random ergodic theorems. When the r random parameters are shifted by the r 0 -shift transformation with r 0 { 1 , 2 , , r } , the major finding is that the (random) ergodic limit functions determined in random ergodic theorems depend essentially only on the r r 0 random parameters. Some of the results obtained here improve the earlier random ergodic theorems of Ryll-Nardzewski (1954), Gladysz (1956), Cairoli (1964), and Yoshimoto (1977) for positive linear contractions on L 1 and Woś (1982) for sub-Markovian operators. Moreover, applications of these results to nonlinear random ergodic theorems for affine operators are also included. Some examples are given for illustrating the relationship between the ergodic limit functions and the random parameters in random ergodic theorems.

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Takeshi Yoshimoto. "On the Dependence of the Limit Functions on the Random Parameters in Random Ergodic Theorems." Abstr. Appl. Anal. 2013 (SI59) 1 - 13, 2013. https://doi.org/10.1155/2013/503689

Information

Published: 2013
First available in Project Euclid: 26 February 2014

zbMATH: 1384.60066
MathSciNet: MR3039159
Digital Object Identifier: 10.1155/2013/503689

Rights: Copyright © 2013 Hindawi

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