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ON NEW FORMS OF THE ERGODIC THEOREM
"... 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
 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
"... Abstract. We present a simple proof of Kingman’s Subadditive Ergodic Theorem that does not rely on Birkhoff’s (Additive) Ergodic Theorem and therefore 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 Theorem that does not rely on Birkhoff’s (Additive) Ergodic Theorem and therefore 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
"... 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 nonstandard 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 nonstandard analysis proof. 1.
CYCLICAL MONOTONICITY AND THE ERGODIC THEOREM
"... Abstract. It is well known that optimal transport plans are cyclically monotone. The reverse implication that cyclically monotone transport plans are optimal needs some assumptions and the proof is nontrivial even if the costs are given by the squared euclidean distance on Rn. We establish this re ..."
THE ERGODIC THEOREM IN L2
"... 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 measurepreserving map. The invariant sigmaalgebra, 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 measurepreserving map. The invariant sigmaalgebra, is the set I of all events A ∈ F such that µ(A4T−1(A)) = 0. We say
A Marginal Ergodic Theorem
 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
"... . 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 meansquare 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
 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 HardyLittlewood method of exponential sums developed by Birch and Davenport
ERGODIC THEOREMS FOR ACTIONS OF HYPERBOLIC GROUPS
"... 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
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