Ergodic Theorems

  • Robert M. Gray


The basic ergodic theorems are proved showing that asymptotic mean stationarity is a sufficient as well as necessary condition for a random process or dynamical system to have convergent sample averages for all bounded measurements. Conditions are found for the convergence of unbounded sample averages in both the almost everywhere and mean sense. The proof follows the coding-flavored proofs developed in the ergodic theory literature in the 1970s rather than the classical route of the maximal ergodic theorem.


Sample Average Ergodic Theorem Ergodic Measure Ergodic Property Invariant Event 
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Copyright information

© Springer-Verlag US 2009

Authors and Affiliations

  1. 1.Department of Electrical EngineeringStanford UniversityStanfordUSA

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