We derive the boundary condition for a subdiffusive particle interacting with a reactive boundary with a finite reaction rate. Molecular crowding conditions, that are found to cause subdiffusion of larger molecules in biological cells, are shown to effect long-tailed distributions with an identical exponent for both the unbinding times from the boundary to the bulk and the rebinding times from ...

The explicit criteria, collected in Tables 5.1 and 5.2, for several types of ergodicity of onedimensional diffusions or birth-death processes have been found out recently in a surprisingly short period. One of the criteria is for exponential ergodicity of birth-death processes. This problem has been opened for a long time in the study of Markov chains. The survey article explains in details the...

We identify conditions for geometric ergodicity of general, and possibly nonparametric, nonlinear autoregressive time series. We also indicate how a condition for ergodicity, with minimal side assumptions, may in fact imply geometric ergodicity. Our examples include models for which exponential stability of the associated (noiseless) dynamical system is not sufficient or not necessary, or both.

We prove absence of infinite clusters and contours in a class critical constrained percolation models on the square lattice. The configuration is assumed to satisfy certain hard local constraints, but only weak symmetry ergodicity conditions are imposed its law. proofs use new combinatorial techniques exploiting planar duality. Applications include diagonal edges for dimer square-octagon latt...

In both estimation and calibration studies, the notion of ergodicity plays a fundamental role, permitting time series averages to be regarded as approximations to population means. As it turns out, many economic models routinely used for quantitative modeling do not satisfy the classical ergodicity conditions. In this paper we develop a new set of ergodicity conditions orientated towards econom...

Ergodicity coefficients for stochastic matrices determine inclusion regions for subdominant eigenvalues; estimate the sensitivity of the stationary distribution to changes in the matrix; and bound the convergence rate of methods for computing the stationary distribution. We survey results for ergodicity coefficients that are defined by p-norms, for stochastic matrices as well as for general rea...

We study experimentally nodal domains of wave functions (electric field distributions) lying in the regime of Breit–Wigner ergodicity in the chaotic microwave half-circular ray-splitting rough billiard. Using the rough billiard without ray-splitting properties we also study the wave functions lying in the regime of Shnirelman ergodicity. The wave functions ΨN of the ray-splitting billiard were ...

In this paper, we introduce a weak form of amenability on topological semigroups that call $$\varphi $$ -amenability, where is character semigroup. Some basic properties new notion are obtained and by giving some examples, show definition weaker than the semigroups. As noticeable result, for semigroup S, it shown if S -amenable, then amenable. Moreover, -ergodicity introduced proved under condi...