Stationarity and ergodicity are desirable properties of any stochastic simulation model for small-scale mobile radio channels. These properties enable the channel simulator to accurately emulate the channel’s statistical properties in a single simulation run without requiring information on the time origin. In a previous paper, we analyzed the ergodicity with respect to (w.r.t.) the autocorrela...

Abstract. This paper surveys various results about Markov chains on general (noncountable) state spaces. It begins with an introduction to Markov chain Monte Carlo (MCMC) algorithms, which provide the motivation and context for the theory which follows. Then, sufficient conditions for geometric and uniform ergodicity, along with quantitative bounds on the rate of convergence to stationarity in ...

We present a dynamical technique for sampling the canonical measure in molecular dynamics. The method controls temperature by use of a device similar to that of Nosé dynamics, but adds random noise to improve ergodicity. In contrast to Langevin dynamics, where noise is added directly to each physical degree of freedom, our method relies on an indirect coupling to a single Brownian particle. For...

For any stochastic matrix A of order n, denote its eigenvalues as λ1(A), . . . , λn(A), ordered so that 1 = |λ1(A)| ≥ |λ2(A)| ≥ . . . ≥ |λn(A)|. Let cT be a row vector of order n whose entries are nonnegative numbers that sum to n. Define S(c), to be the set of n × n row-stochastic matrices with column sum vector cT . In this paper the quantity λ(c) = max{|λ2(A)||A ∈ S(c)} is considered. The ve...

This paper surveys various results about Markov chains on general (non-countable) state spaces. It begins with an introduction to Markov chain Monte Carlo (MCMC) algorithms, which provide the motivation and context for the theory which follows. Then, sufficient conditions for geometric and uniform ergodicity are presented, along with quantitative bounds on the rate of convergence to stationarit...

Let P be the set of C1 partially hyperbolic volume-preserving flows with one dimensional central direction endowed with the C1flow topology. We prove that any X ∈ P can be approximated by an ergodic C2 volume-preserving flow. As a consequence ergodicity is dense in P. MSC 2000: primary 37D30, 37D25; secondary 37A99. keywords: Dominated splitting; Partial hyperbolicity; Volume-preserving flows; ...

In this paper, we consider a general family of asymmetric volatility models with stationary and ergodic coefficients. This family can nest several non-linear asymmetric GARCH models with stochastic parameters into its ambit. It also generalizes Markovswitching GARCH and GJR models. The geometric ergodicity of the proposed process is established. Sufficient conditions for stationarity and existe...

We introduce a new property of Markov chains, called variance bounding. We prove that, for reversible chains at least, variance bounding is weaker than, but closely related to, geometric ergodicity. Furthermore, variance bounding is equivalent to the existence of usual central limit theorems for all L2 functionals. Also, variance bounding (unlike geometric ergodicity) is preserved under the Pes...

We introduce a new property of Markov chains, called variance bounding. We prove that, for reversible chains at least, variance bounding is weaker than, but closely related to, geometric ergodicity. Furthermore, variance bounding is equivalent to the existence of usual central limit theorems for all L functionals. Also, variance bounding (unlike geometric ergodicity) is preserved under the Pesk...

Quantum ergodicity, which expresses the semiclassical convergence of almost all expectation values of observables in eigenstates of the quantum Hamiltonian to the corresponding classical microcanonical average, is proven for non-relativistic quantum particles with spin 1/2. It is shown that quantum ergodicity holds, if a suitable combination of the classical translational dynamics and the spin ...