A non-conventional ergodic theorem for a nilsystem

A Non Conventional Ergodic Theorem for a Nil-System

We prove a non conventional pointwise convergence theorem for a nilsystem, and give an explicit formula for the limit.

A Ratio Ergodic Theorem for Multiparameter Non-singular Actions

We prove a ratio ergodic theorem for non-singular free Z and R actions, along balls in an arbitrary norm. Using a Chacon-Ornstein type lemma the proof is reduced to a statement about the amount of mass of a probability measure that can concentrate on (thickened) boundaries of balls in R. The proof relies on geometric properties of norms, including the Besicovitch covering lemma and the fact tha...

A Mean Ergodic Theorem For Asymptotically Quasi-Nonexpansive Affine Mappings in Banach Spaces Satisfying Opial's Condition

A Marginal Ergodic Theorem

Michael Lavine Duke University, Durham, NC, USA. Summary. In recent years there have been several papers giving examples of Markov Chain Monte Carlo (MCMC) algorithms whose invariant measures are improper (have infinite mass) and which therefore are not positive recurrent, yet which have subchains from which valid inference can be derived. These are nonergodic (not having a limiting distributio...

A Quasi-ergodic Theorem for Evanescent Processes

We prove a conditioned version of the ergodic theorem for Markov processes, which we call a quasi-ergodic theorem. We also prove a convergence result for conditioned processes as the conditioning event becomes rarer.