We consider the problem of Lp-consistent density estimation from the initial segments of strongly dependent processes. It is shown that no procedure can consistently estimate the one-dimensional marginal density of every stationary ergodic process for which such a density exists. A similar result is established for the problem of estimating the support of the marginal distribution of an ergodic...

The classical Poisson functor associates to every infinite measure preserving dynamical system (X, μ, T) a probability (X*, μ*, T*) called the suspension of T. In this paper we generalize construction: subgroup Aut2(X, μ) μ-nonsingular transformations T X is specified as largest for which T* μ*-nonsingular. topological structure studied. We show that generic element in ergodic and Krieger type ...

The general expressions for the time-dependent ensemble averages of the second spatial moments ^A& and the effective dispersivities g, defined as (1/ 2m)(d^A&/dt) where m is the magnitude of the mean flow velocity m, are evaluated in order to study the effect of initial plume size on ^A& and g in three-dimensional heterogeneous isotropic aquifers under the first-order approximation to the parti...

Let f be a real-valued function defined on the phase space of a dynamical system. Ergodic optimization is the study of those orbits, or invariant probability measures, whose ergodic f -average is as large as possible. In these notes we establish some basic aspects of the theory: equivalent definitions of the maximum ergodic average, existence and generic uniqueness of maximizing measures, and t...

In cryptography and coding theory, it is important to study the pseudo-random sequences and the ergodic transformations. We already have the 1-Lipshitz ergodic theory over Z2 established by V. Anashin and others. In this paper we present an ergodic theory over F2[[T ]] and some ideas which might be very useful in applications.

We study a stability property of probability laws with respect to small violations of algorithmic randomness. A sufficient condition of stability is presented in terms of Schnorr tests of algorithmic randomness. Most probability laws, like the strong law of large numbers, the law of iterated logarithm, and even Birkhoff’s pointwise ergodic theorem for ergodic transformations, are stable in this...

We introduce a formalism for handling general spaces of hierarchical tilings, a category that includes substitution tilings, Bratteli-Vershik systems, S-adic transformations, and multi-dimensional cut-and-stack transformations. We explore ergodic, spectral and topological properties of these spaces. We show that familiar properties of substitution tilings carry over under appropriate assumption...

We investigate ergodic theory of Poisson suspensions. In the process, we establish close connections between finite and infinite measure preserving ergodic theory. Poisson suspensions thus provide a new approach to infinite measure preserving ergodic theory. Fields investigated here are mixing properties, spectral theory, joinings. We also compare Poisson suspensions to the apparently similar l...

In this paper, Kolmogorov-Sinai entropy is studied using mathematical modeling of an observer $ Theta $. The relative entropy of a sub-$ sigma_Theta $-algebra having finite atoms is defined and then   the ergodic properties of relative  semi-dynamical systems are investigated.  Also,  a relative version of Kolmogorov-Sinai theorem  is given. Finally, it is proved  that the relative entropy of a...