We consider the extent to which Markov chain convergence properties are affected by the presence of computer floating-point roundoff error. Both geometric ergodicity and polynomial ergodicity are considered. This paper extends previous work of Roberts, Rosenthal, and Schwartz (1998); connections between that work and the present paper are discussed.

Relationships between ergodicity and structures of fourthorder spectral moments are investigated. In particular it is shown that second-order ergodicity of a random process is directly related to the distribution of these moments on the normal manifolds of the frequency domain. This result is illustrated by various examples.

We derive sufficient conditions for subgeometric f -ergodicity of strongly Markovian processes. We first propose a criterion based on modulated moment of some delayed return-time to a petite set. We then formulate a criterion for polynomial f -ergodicity in terms of a drift condition on the generator. Applications to specific processes are considered, including Langevin tempered diffusions on R...

Numerical simulations have shown that certain driven nonlinear systems can be characterized by mean-field statistical properties often associated with ergodic dynamics [C. D. Ferguson, W. Klein, and J. B. Rundle, Phys. Rev. E 60, 1359 (1999); D. Egolf, Science 287, 101 (2000)]. These driven mean-field threshold systems feature long-range interactions and can be treated as equilibriumlike system...

A simple proof and detailed analysis on the non-ergodicity for multidimensional harmonic oscillator systems with Nose-Hoover type thermostat are given. The origin of nonergodicity is symmetries in target physical system, differ from that 1-dimensional oscillator. new deterministic method to recover ergodicity also presented. An individual variable attached each degree freedom, all these variabl...

We establish new conditions for obtaining uniform bounds on the moments of discrete-time stochastic processes. Our results require a weak negative drift criterion along with state-dependent restriction centered conditional process. They, in particular, generalize main result [22] which requires constant bound averaged one-step jumps The feature our make them suitable large class multiplicative-...

Golay has used the ergodicity postulate to calculate that the merit factor F of a Legendre sequence offset by a fraction f of its length has an asymptotic value given by l/F= (2/3)-41fj+ 8f2, IfI I l/2, which gives F= 6 for IfI =1/4. Here this is proved without using the ergodicity postulate.

We study the problem of lifting ergodicity to certain skew-product extensions over shifts of nite type. This can be done by computing the asymptotic range of the deening cocycle. For a class of ergodic shift-invariant measures and a class of functions (deening conservative extensions) we give a characterisation of ergodicity in terms of weights of periodic orbits in the shift space.

We prove that the stationarity and the ergodicity of a quantum source {ρ[1,m]}m=1 are preserved by any trace-preserving completely positive linear map of the tensor product form E⊗m, where a copy of E acts locally on each spin lattice site. We also establish ergodicity criteria for so called classically-correlated quantum sources.