Coboundaries in
Cohomology groups, multipliers and factors in ergodic theory
The problem of compact factors in ergodic theory and its relationship with the problem of extending a cocycle to a cocycle of a larger action are studied.
Compact abelian group extensions of dynamical systems II
Compactness of trajectories of dynamical systems in complete uniform spaces
Comparison between criteria leading to the weak invariance principle
The aim of this paper is to compare various criteria leading to the central limit theorem and the weak invariance principle. These criteria are the martingale-coboundary decomposition developed by Gordin in Dokl. Akad. Nauk SSSR188 (1969), the projective criterion introduced by Dedecker in Probab. Theory Related Fields110 (1998), which was subsequently improved by Dedecker and Rio in Ann. Inst. H. Poincaré Probab. Statist.36 (2000) and the condition introduced by Maxwell and Woodroofe in Ann. Probab.28...
Complete positivity of entropy and non-Bernoullicity for transformation groups
The existence of non-Bernoullian actions with completely positive entropy is proved for a class of countable amenable groups which includes, in particular, a class of Abelian groups and groups with non-trivial finite subgroups. For this purpose, we apply a reverse version of the Rudolph-Weiss theorem.
Conditions d'isomorphisme des flots spéciaux
Consistency of the LSE in Linear regression with stationary noise
We obtain conditions for L₂ and strong consistency of the least square estimators of the coefficients in a multi-linear regression model with a stationary random noise. For given non-random regressors, we obtain conditions which ensure L₂-consistency for all wide sense stationary noise sequences with spectral measure in a given class. The condition for the class of all noises with continuous (i.e., atomless) spectral measures yields also -consistency when the noise is strict sense stationary with...
Construction de cocycles en escalier ergodiques et faiblement mélangeants au-dessus de rotations irrationnelles du cercle
Construction of non-constant and ergodic cocycles
We construct continuous G-valued cocycles that are not cohomologous to any compact constant via a measurable transfer function, provided the underlying dynamical system is rigid and the range group G satisfies a certain general condition. For more general ergodic aperiodic systems, we also show that the set of continuous ergodic cocycles is residual in the class of all continuous cocycles provided the range group G is a compact connected Lie group. The first construction is based on the "closure...
Constructions of cocycles over irrational rotations
We construct a coboundary cocycle which is of bounded variation, is homotopic to the identity and is Hölder continuous with an arbitrary Hölder exponent smaller than 1.
Constructions of smooth and analytic cocycles over irrational circle rotations
We define a class of step cocycles (which are coboundaries) for irrational rotations of the unit circle and give conditions for their approximation by smooth and real analytic coboundaries. The transfer functions of the approximating (smooth and real analytic) coboundaries are close (in the supremum norm) to the transfer functions of the original ones. This result makes it possible to construct smooth and real analytic cocycles which are ergodic, ergodic and squashable (see [Aaronson, Lemańczyk,...
Contribución al estudio de la teoría ergódica de procesos aleatorios con valores en espacios métricos compactos.
Convergence des moyennes ergodiques pour des sous-suites
Convergence of Continued Fraction Type Algorithms and Generators.
Convergence of the averages and finiteness of ergodic power funtions in weighted L1 spaces.
Let (X, F, μ) be a finite measure space. Let T: X → X be a measure preserving transformation and let Anf denote the average of Tkf, k = 0, ..., n. Given a real positive function v on X, we prove that {Anf} converges in the a.e. sense for every f in L1(v dμ) if and only if infi ≥ 0 v(Tix) > 0 a.e., and the same condition is equivalent to the finiteness of a related ergodic power function Prf for every f in L1(v dμ). We apply this result to characterize, being T null-preserving, the finite...
Convergence of the -series for stationary sequences.
Convolutions related to q-deformed commutativity
Two important examples of q-deformed commutativity relations are: aa* - qa*a = 1, studied in particular by M. Bożejko and R. Speicher, and ab = qba, studied by T. H. Koornwinder and S. Majid. The second case includes the q-normality of operators, defined by S. Ôta (aa* = qa*a). These two frameworks give rise to different convolutions. In particular, in the second scheme, G. Carnovale and T. H. Koornwinder studied their q-convolution. In the present paper we consider another convolution of measures...
Coordinatewise decomposition, Borel cohomology, and invariant measures
Given Polish spaces X and Y and a Borel set S ⊆ X × Y with countable sections, we describe the circumstances under which a Borel function f: S → ℝ is of the form f(x,y) = u(x) + v(y), where u: X → ℝ and v: Y → ℝ are Borel. This turns out to be a special case of the problem of determining whether a real-valued Borel cocycle on a countable Borel equivalence relation is a coboundary. We use several Glimm-Effros style dichotomies to give a solution to this problem in terms of certain σ-finite measures...
Correction to An algebraic formulation of ergodic problems