The statistical properties of endomorphisms under the assumption that the associated Perron– Frobenius operator is quasicompact are considered. In particular, the central limit theorem, weak invariance principle and law of the iterated logarithm for sufficiently regular observations are examined. The approach clarifies the role of the usual assumptions of ergodicity, weak mixing, and exactness....

We present counter-examples to demonstrate that when g is unbounded the conditions of Simultaneous Uniform Ergodicity and Diminishing Adaptation are not enough to guarantee that the the weak law of large numbers (WLLN) holds, although from the results of Roberts and Rosenthal [4] we know that WLLN holds under these conditions when g is bounded. Then we show various theoretical results of the WL...

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...