Displaying similar documents to “Support overlapping L 1 contractions and exact non-singular transformations”

Multiparameter pointwise ergodic theorems for Markov operators on L.

Ryotaro Sato (1994)

Publicacions Matemàtiques

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Let P1, ..., Pd be commuting Markov operators on L∞(X,F,μ), where (X,F,μ) is a probability measure space. Assuming that each Pi is either conservative or invertible, we prove that for every f in Lp(X,F,μ) with 1 ≤ p < ∞ the averages Anf = (n + 1)-d Σ0≤ni≤n P1

Ergodic properties of skew products with Lasota-Yorke type maps in the base

Zbigniew Kowalski (1993)

Studia Mathematica

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We consider skew products T ( x , y ) = ( f ( x ) , T e ( x ) y ) preserving a measure which is absolutely continuous with respect to the product measure. Here f is a 1-sided Markov shift with a finite set of states or a Lasota-Yorke type transformation and T i , i = 1,..., max e, are nonsingular transformations of some probability space. We obtain the description of the set of eigenfunctions of the Frobenius-Perron operator for T and consequently we get the conditions ensuring the ergodicity, weak mixing and exactness of T....

On the classification of Markov chains via occupation measures

Onésimo Hernández-Lerma, Jean Lasserre (2000)

Applicationes Mathematicae

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We consider a Markov chain on a locally compact separable metric space X and with a unique invariant probability. We show that such a chain can be classified into two categories according to the type of convergence of the expected occupation measures. Several properties in each category are investigated.

Strong and weak stability of some Markov operators

Ryszard Rudnicki (2000)

Colloquium Mathematicae

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An integral Markov operator P appearing in biomathematics is investigated. This operator acts on the space of probabilistic Borel measures. Let μ and ν be probabilistic Borel measures. Sufficient conditions for weak and strong convergence of the sequence ( P n μ - P n ν ) to 0 are given.

Ergodic properties of skew products withfibre maps of Lasota-Yorke type

Zbigniew Kowalski (1994)

Applicationes Mathematicae

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We consider the skew product transformation T(x,y)= (f(x), T e ( x ) ) where f is an endomorphism of a Lebesgue space (X,A,p), e : X → S and T s s ∈ S is a family of Lasota-Yorke type maps of the unit interval into itself. We obtain conditions under which the ergodic properties of f imply the same properties for T. Consequently, we get the asymptotical stability of random perturbations of a single Lasota-Yorke type map. We apply this to some probabilistic model of the motion of cogged bits in the rotary...