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Displaying 61 – 80 of 123

Note on the isomorphism problem for weighted unitary operators associated with a nonsingular automorphism

K. Frączek, M. Wysokińska (2008)

Colloquium Mathematicae

We give a negative answer to a question put by Nadkarni: Let S be an ergodic, conservative and nonsingular automorphism on $(X ̃,_{X ̃}, m)$ . Consider the associated unitary operators on $L ² (X ̃,_{X ̃}, m)$ given by $U ̃_{S} f = \sqrt (d (m \circ S) / d m) \cdot (f \circ S)$ and $φ \cdot U ̃_{S}$ , where φ is a cocycle of modulus one. Does spectral isomorphism of these two operators imply that φ is a coboundary? To answer it negatively, we give an example which arises from an infinite measure-preserving transformation with countable Lebesgue spectrum.

On a nonstandard approach to invariant measures for Markov operators

Andrzej Wiśnicki (2010)

Annales UMCS, Mathematica

We show the existence of invariant measures for Markov-Feller operators defined on completely regular topological spaces which satisfy the classical positivity condition.

On absorption times and Dirichlet eigenvalues

Laurent Miclo (2010)

ESAIM: Probability and Statistics

This paper gives a stochastic representation in spectral terms for the absorption time T of a finite Markov chain which is irreducible and reversible outside the absorbing point. This yields quantitative informations on the parameters of a similar representation due to O'Cinneide for general chains admitting real eigenvalues. In the discrete time setting, if the underlying Dirichlet eigenvalues (namely the eigenvalues of the Markov transition operator restricted to the functions vanishing on...

On certain weighted moving averages and their differentiation analogues.

Avramidou, Parthena (2006)

The New York Journal of Mathematics [electronic only]

On dependence structure of copula-based Markov chains

Martial Longla (2014)

ESAIM: Probability and Statistics

We consider dependence coefficients for stationary Markov chains. We emphasize on some equivalencies for reversible Markov chains. We improve some known results and provide a necessary condition for Markov chains based on Archimedean copulas to be exponential ρ-mixing. We analyse the example of the Mardia and Frechet copula families using small sets.

On embeddability of automorphisms into measurable flows from the point of view of self-joining properties

Joanna Kułaga-Przymus (2015)

Fundamenta Mathematicae

We compare self-joining and embeddability properties. In particular, we prove that a measure preserving flow ${(T_{t})}_{t \in ℝ}$ with T₁ ergodic is 2-fold quasi-simple (resp. 2-fold distally simple) if and only if T₁ is 2-fold quasi-simple (resp. 2-fold distally simple). We also show that the Furstenberg-Zimmer decomposition for a flow ${(T_{t})}_{t \in ℝ}$ with T₁ ergodic with respect to any flow factor is the same for ${(T_{t})}_{t \in ℝ}$ and for T₁. We give an example of a 2-fold quasi-simple flow disjoint from simple flows and whose time-one map is...

On iterates of strong Feller operators on ordered phase spaces

Wojciech Bartoszek (2004)

Colloquium Mathematicae

Let (X,d) be a metric space where all closed balls are compact, with a fixed σ-finite Borel measure μ. Assume further that X is endowed with a linear order ⪯. Given a Markov (regular) operator P: L¹(μ) → L¹(μ) we discuss the asymptotic behaviour of the iterates Pⁿ. The paper deals with operators P which are Feller and such that the μ-absolutely continuous parts of the transition probabilities ${P (x, \cdot)}_{x \in X}$ are continuous with respect to x. Under some concentration assumptions on the asymptotic transition probabilities...

On new spectral multiplicities for ergodic maps

Alexandre I. Danilenko (2010)

Studia Mathematica

It is shown that each subset of positive integers that contains 2 is realizable as the set of essential values of the multiplicity function for the Koopman operator of some weakly mixing transformation.

On some properties of the Lüroth-type alternating series representations for real numbers.

Ganatsiou, C. (2001)

International Journal of Mathematics and Mathematical Sciences

On stability properties of positive contractions of L¹-spaces associated with finite von Neumann algebras

Farrukh Mukhamedov, Hasan Akin, Seyit Temir (2006)

Colloquium Mathematicae

We extend the notion of Dobrushin coefficient of ergodicity to positive contractions defined on the L¹-space associated with a finite von Neumann algebra, and in terms of this coefficient we prove stability results for L¹-contractions.

On the convergence to 0 of mₙξmod 1

Bassam Fayad, Jean-Paul Thouvenot (2014)

Acta Arithmetica

We show that for any irrational number α and a sequence ${m_{l}}_{l \in ℕ}$ of integers such that $l i m_{l \to \infty} | | | m_{l} α | | | = 0$ , there exists a continuous measure μ on the circle such that $l i m_{l \to \infty} \int_{} | | | m_{l} θ | | | d μ (θ) = 0$ . This implies that any rigidity sequence of any ergodic transformation is a rigidity sequence for some weakly mixing dynamical system. On the other hand, we show that for any α ∈ ℝ - ℚ, there exists a sequence ${m_{l}}_{l \in ℕ}$ of integers such that $| | | m_{l} α | | | \to 0$ and such that $m_{l} θ [1]$ is dense on the circle if and only if θ ∉ ℚα + ℚ.

On the dynamical meaning of spectral dimensions

Italo Guarneri (1998)

Annales de l'I.H.P. Physique théorique

On the individual ergodic theorem in $D$ -posets of fuzzy sets

Beloslav Riečan (2000)

Czechoslovak Mathematical Journal

Calculus for observables in a space of functions from an abstract set to the unit interval is developed and then the individual ergodic theorem is proved.

On the location of poles of Ruelle's zeta function for Gauss map

Dieter H. Mayer (1989)

Banach Center Publications

On the “zero-two” law for positive contractions in the Banach-Kantorovich lattice $L^{p} (\nabla, μ)$

Inomjon Ganiev, Farrukh Mukhamedov (2006)

Commentationes Mathematicae Universitatis Carolinae

In the present paper we prove the “zero-two” law for positive contractions in the Banach-Kantorovich lattices $L^{p} (\nabla, μ)$ , constructed by a measure $μ$ with values in the ring of all measurable functions.

Orthogonality and probability: mixing times.

Kovchegov, Yevgeniy V. (2010)

Electronic Communications in Probability [electronic only]

Piecewise-deterministic Markov processes

Jolanta Kazak (2013)

Annales Polonici Mathematici

Poisson driven stochastic differential equations on a separable Banach space are examined. Some sufficient conditions are given for the asymptotic stability of a Markov operator P corresponding to the change of distribution from jump to jump. We also give criteria for the continuous dependence of the invariant measure for P on the intensity of the Poisson process.

Pointwise asymptotics for the jumps of ergodic averages.

Catuogno, P. J., Ferrando, S. E. (2001)

The New York Journal of Mathematics [electronic only]

Pointwise convergence for subsequences of weighted averages

Patrick LaVictoire (2011)

Colloquium Mathematicae

We prove that if μₙ are probability measures on ℤ such that μ̂ₙ converges to 0 uniformly on every compact subset of (0,1), then there exists a subsequence $n_{k}$ such that the weighted ergodic averages corresponding to $μ_{n_{k}}$ satisfy a pointwise ergodic theorem in L¹. We further discuss the relationship between Fourier decay and pointwise ergodic theorems for subsequences, considering in particular the averages along n² + ⌊ρ(n)⌋ for a slowly growing function ρ. Under some monotonicity assumptions, the rate...

Pointwise convergence of nonconventional averages

I. Assani (2005)

Colloquium Mathematicae

We answer a question of H. Furstenberg on the pointwise convergence of the averages $1 / N \sum_{n = 1}^{N} U ⁿ (f \cdot R ⁿ (g))$ , where U and R are positive operators. We also study the pointwise convergence of the averages $1 / N \sum_{n = 1}^{N} f (S ⁿ x) g (R ⁿ x)$ when T and S are measure preserving transformations.

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