Abstract. We introduce an algorithm based on semidefinite programming that yields increasing (resp., decreasing) sequences of lower (resp., upper) bounds on polynomial stationary averages of di↵usions with polynomial drift vector and di↵usion coe cients. The bounds are obtained by optimizing an objective, determined by the stationary average of interest, over the set of real vectors defined by ...

This is the second paper in a series concerning the study of steady states, including stationary solutions and measures, of a Fokker-Planck equation in a general domain in R with Lp̄loc drift term and W 1,p̄ loc diffusion term for any p̄ > n. In this paper, we obtain some non-existence results of stationary measures under conditions involving anti-Lyapunov type of functions associated with the sta...

Invariant measures of dynamical systems generated e. g. by difference equations can be computed by discretizing the originally continuum state space, and replacing the action of the generator by the transition mechanism of a Markov chain. In fact they are approximated by stationary vectors of these Markov chains. Here we extend this well known approximation result and the underlying algorithm t...

A measure of the “mixing time” or “time to stationarity” in a finite irreducible discrete time Markov chain is considered. The statistic η π i ij j m j m = = ∑ 1 , where {πj} is the stationary distribution and mij is the mean first passage time from state i to state j of the Markov chain, is shown to be independent of the state i that the chain starts in (so that ηi = η for all i), is minimal i...

We investigate the following extendability problem for systems, for which the available information is given by a monotone set mapping M on the field CT of measurable cylinders of a product ample space (XT ,RT ): given that M is invariant under a RT −RT measurable transformation H of XT , i.e. M(H−1(B)) = M(B) for all B ∈ CT , is it possible to find H-invariant monotone extensions of M to the p...

We study a discrete-time quantum walk (QW) on the line with a single phase at the origin which was introduced and studied by Wojcik et al.[1]. We call the model “the Wojcik model” here. Konno et al.[2] investigated other types of QWs with one defect at the origin. They presented a method which gives the stationary measure corresponding to localization for the QWs by use of the generating functi...

This paper offers a way to construct a locally optimal stationary approximation for a non-stationary Gaussian process. In cases where this construction leads to a unique stationary approximation we call it a stationary tangent. This is the case with Gaussian processes governed by smooth n-dimensional correlations. We associate these correlations with equivalence classes of curves in R. These ar...

In a multi-type totally asymmetric simple exclusion process (TASEP) on the line, each site of Z is occupied by a particle labeled with a number and two neighboring particles are interchanged at rate one if their labels are in increasing order. Consider the process with the initial configuration where each particle is labeled by its position. It is known that in this case a.s. each particle has ...

We are going to give necessary and sufficient conditions for a multivari-ate stationary stochastic process to be completely regular. We also give the answer to a question of V.V. Peller concerning the spectral measure characterization of such processes.

We prove that a stationary extrinsic (or intrinsic, respectively) biharmonic map u 2 W ( ; N) from R into a Riemnanian manifold N is smooth away from a closed set of (m 4)-dimensional Hausdor measure zero. x