scholarly journals A ratio ergodic theorem for multiparameter non-singular actions

2010 ◽  
pp. 365-383 ◽  
Author(s):  
Michael Hochman
Keyword(s):  
Ergodic Theorem ◽  
Ratio Ergodic Theorem

Induced transformations of recurrent a.m.s. dynamical systems

2015 ◽  
Vol 15 (02) ◽  
pp. 1550010
Author(s):  
Sheng Huang ◽  
Mikael Skoglund
Keyword(s):  
Dynamical System ◽  
Dynamical Systems ◽  
Random Process ◽  
Ergodic Theorem ◽  
Finite Measure ◽  
Stationary Random Process ◽  
Finite State ◽  
Ratio Ergodic Theorem

This note proves that an induced transformation with respect to a finite measure set of a recurrent asymptotically mean stationary dynamical system with a sigma-finite measure is asymptotically mean stationary. Consequently, the Shannon–McMillan–Breiman theorem, as well as the Shannon–McMillan theorem, holds for all reduced processes of any finite-state recurrent asymptotically mean stationary random process. As a by-product, a ratio ergodic theorem for asymptotically mean stationary dynamical systems is presented.

scholarly journals On the ratio ergodic theorem for semi-groups

1971 ◽  
Vol 39 (3) ◽  
pp. 659-667 ◽  
Author(s):  
Humphrey Fong ◽  
Louis Sucheston
Keyword(s):  
Ergodic Theorem ◽  
Ratio Ergodic Theorem

scholarly journals A horospherical ratio ergodic theorem for actions of free groups

2014 ◽  
Vol 8 (2) ◽  
pp. 331-353 ◽  
Author(s):  
Lewis Bowen ◽  
Amos Nevo
Keyword(s):  
Ergodic Theorem ◽  
Free Groups ◽  
Ratio Ergodic Theorem

scholarly journals A general ratio ergodic theorem for semigroups

1976 ◽  
Vol 62 (2) ◽  
pp. 435-437
Author(s):  
Shigeru Hasegawa ◽  
Ryōtarō Satō
Keyword(s):  
Ergodic Theorem ◽  
Ratio Ergodic Theorem
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