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ON NEW FORMS OF THE ERGODIC THEOREM

by V. V. Kozlov, D. V. Treschev
"... Abstract. We present generalizations of the classical Birkhoff and von Neumann ergodic theorems, where the time average is replaced by a more general average, including some density. 1. ..."
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Abstract. We present generalizations of the classical Birkhoff and von Neumann ergodic theorems, where the time average is replaced by a more general average, including some density. 1.

Ergodic theorems in demography

by E. Cohen - Math. Proc. Cambridge Philos
"... ABSTRACT. The ergodic theorems of demography describe the properties of a product of certain nonnegative matrices, in the limit as the number of matrix factors in the product becomes large. This paper reviews these theorems and, where possible, their empirical usefulness. The strong ergodic theorem ..."
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ABSTRACT. The ergodic theorems of demography describe the properties of a product of certain nonnegative matrices, in the limit as the number of matrix factors in the product becomes large. This paper reviews these theorems and, where possible, their empirical usefulness. The strong ergodic theorem

ON THE SUBADDITIVE ERGODIC THEOREM

by Artur Avila, Jairo Bochi
"... Abstract. We present a simple proof of Kingman’s Subadditive Ergodic The-orem that does not rely on Birkhoff’s (Additive) Ergodic Theorem and there-fore yields it as a corollary. 1. Statements Throughout this note, let (X,A, µ) be a fixed probability space and T: X → X be a fixed measurable map that ..."
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Abstract. We present a simple proof of Kingman’s Subadditive Ergodic The-orem that does not rely on Birkhoff’s (Additive) Ergodic Theorem and there-fore yields it as a corollary. 1. Statements Throughout this note, let (X,A, µ) be a fixed probability space and T: X → X be a fixed measurable map

BIRKHOFF ERGODIC THEOREM

by unknown authors
"... Abstract. We will give a proof of the pointwise ergodic theorem, which was first proved by Birkhoff. Many improvements have been made since Birkhoff’s orginal proof. The version we give here is due to Keane and Petersen, which builds on the Kamae’s non-standard analysis proof. 1. ..."
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Abstract. We will give a proof of the pointwise ergodic theorem, which was first proved by Birkhoff. Many improvements have been made since Birkhoff’s orginal proof. The version we give here is due to Keane and Petersen, which builds on the Kamae’s non-standard analysis proof. 1.

CYCLICAL MONOTONICITY AND THE ERGODIC THEOREM

by unknown authors
"... Abstract. It is well known that optimal transport plans are cyclically mono-tone. The reverse implication that cyclically monotone transport plans are optimal needs some assumptions and the proof is non-trivial even if the costs are given by the squared euclidean distance on Rn. We establish this re ..."
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this result as a corollary to the ergodic theorem. 1.

THE ERGODIC THEOREM IN L2

by unknown authors
"... Abstract. We prove von Neumann’s L2 ergodic theorem, and conditional expectation. 1. Von Neumann’s mean ergodic theorem Let (Ω,F, µ) be a probability space and let T: Ω → Ω be a measure-preserving map. The invariant sigma-algebra, is the set I of all events A ∈ F such that µ(A4T−1(A)) = 0. We say t ..."
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Abstract. We prove von Neumann’s L2 ergodic theorem, and conditional expectation. 1. Von Neumann’s mean ergodic theorem Let (Ω,F, µ) be a probability space and let T: Ω → Ω be a measure-preserving map. The invariant sigma-algebra, is the set I of all events A ∈ F such that µ(A4T−1(A)) = 0. We say

A Marginal Ergodic Theorem

by Michael Lavine - Bayesian Statistics 7, 577–586 , 2003
"... This paper gives a marginal ergodic theorem which (a) gives conditions on Z guaranteeing that the subchain X is ergodic, (b) gives a formula for computing the limiting distribution in case it exists, and (c) gives a formula for bounding the lim inf and lim sup as n ! 1 of the distribution of X(n) in ..."
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This paper gives a marginal ergodic theorem which (a) gives conditions on Z guaranteeing that the subchain X is ergodic, (b) gives a formula for computing the limiting distribution in case it exists, and (c) gives a formula for bounding the lim inf and lim sup as n ! 1 of the distribution of X

Ergodic Theorems And The Basis Of Science

by Karl Petersen
"... . New results in ergodic theory show that averages of repeated measurements will typically diverge with probability one if there are random errors in the measurement of time. Since mean-square convergence of the averages is not so susceptible to these anomalies, we are led again to compare the me ..."
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the mean and pointwise ergodic theorems and to reconsider efforts to determine properties of a stochastic process from the study of a generic sample path. There are also implications for models of time and the interaction between observer and observable. 1. Introduction Continuing research in ergodic

Diophantine equations and ergodic theorems

by Akos Magyar, Akos Magyar - Amer. J. Math
"... Abstract. Let (X,µ) be a probability measure space and T1,..., Tn be a family of commuting, measure preserving invertible transformations on X. Let Q(m1,..., mn) be a homogeneous, positive polynomial with integer coefficients, and let Sλ = {m ∈ Zn: Q(m) = λ} denote the set of integer solutions m = ..."
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distributed on X w.r.t. µ for a.e. x ∈ X as λ→∞. That is the pointwise ergodic theorem holds when the standard averages are replaced by the ones, where the exponents satisfy a diophantine equation. The proof uses a variant of the Hardy-Littlewood method of exponential sums developed by Birch and Davenport

ERGODIC THEOREMS FOR ACTIONS OF HYPERBOLIC GROUPS

by Mark Pollicott, Richard Sharp
"... Abstract. In this note we give a short proof of a pointwise ergodic theorem for measure preserving actions of word hyperbolic groups, also obtained recently by Bufetov, Khristoforov and Klimenko. Our approach also applies to infinite measure spaces and one application is to linear actions of discret ..."
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Abstract. In this note we give a short proof of a pointwise ergodic theorem for measure preserving actions of word hyperbolic groups, also obtained recently by Bufetov, Khristoforov and Klimenko. Our approach also applies to infinite measure spaces and one application is to linear actions
Results 1 - 10 of 1,165