A nonlinear ergodic theorem for discrete systems

The Uniform Ergodic Theorem for Dynamical Systems

Necessary and sufficient conditions are given for the uniform convergence over an arbitrary index set in von Neumann’s mean and Birkhoff’s pointwise ergodic theorem. Three different types of conditions already known from probability theory are investigated. Firstly it is shown that the property of being eventually totally bounded in the mean is necessary and sufficient. This condition involves ...

Robust Model Predictive Control for a Class of Discrete Nonlinear systems

This paper presents a robust model predictive control scheme for a class of discrete-time nonlinear systems subject to state and input constraints. Each subsystem is composed of a nominal LTI part and an additive uncertain non-linear time-varying function which satisfies a quadratic constraint. Using the dual-mode MPC stability theory, a sufficient condition is constructed for synthesizing the ...

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

Second Order Ergodic Theorem for Self-similar Tiling Systems

We consider infinite measure-preserving non-primitive selfsimilar tiling systems in Euclidean space R. We establish the secondorder ergodic theorem for such systems. The speed of convergence is determined by the Hausdorff dimension of a graph-directed set associated to the substitution rule.