We study the self-averaging properties and ergodicity of the mean square displacement m(t) of particles diffusing in d dimensional quenched random environments which give rise to subdiffusive average motion. These properties are investigated in terms of the sample to sample fluctuations as measured by the variance of m(t). We find that m(t) is not self-averaging for d<2 due to the inefficient d...

In this talk, I will extend Doeblin’s ergodicity coefficient (originally defined for finite dimensional stochastic matrices) to kernels of time-homogenous Markov chains over Polish spaces, and show how a strictly positive Doeblin’s coefficient leads to lowto moderatecomplexity approximations of the occupancy distributions of subsets of the state space. Such approximations may be particularly us...

This paper studies the asymptotic properties of moment estimators for the general shifting level process (SLP). A law of large numbers and a weak convergence theorem are obtained under conditions involving the unobservable processes which make up SLP. Specific conditions about those underlying processes are acided to give explicit results, applicable to a large class of moment estimators. Actua...

For a general attractive Probabilistic Cellular Automata on SZ d , we prove that the (time-) convergence towards equilibrium of this Markovian parallel dynamics, exponentially fast in the uniform norm, is equivalent to a condition (A). This condition means the exponential decay of the in uence from the boundary for the invariant measures of the system restricted to nite boxes. For a class of re...

The notion of a successful coupling of Markov processes, based on the idea that both components of the coupled system “intersect” in finite time with probability one, is extended to cover situations when the coupling is unnecessarily Markovian and its components are only converging (in a certain sense) to each other with time. Under these assumptions the unique ergodicity of the original Markov...

This survey is based on a series of talks I gave at the conference " Dynamical systems and diophantine approximation " at l'Instut Henri Poincaré in June 2003. I will present asymptotic results (transitivity, ergodicity, weak-mixing) for billiards based on the approximation technique developed by Katok and Zemlyakov. I will also present approximation techniques which allow to prove the abundanc...

The Gärtner-Ellis condition for the square of an asymptotically stationary Gaussian process is established. The same limit holds for the conditional distribution given any fixed initial point, which entails weak multiplicative ergodicity. The limit is shown to be the Laplace transform of a convolution of Gamma distributions with Poisson compound of exponentials. A proof based on WienerHopf fact...