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Birkhoff’s Ergodic Theorem
In the context of stochastic processes, ergodic theory relates the long-run “time-averages” such as the sample mean of an evolving strictly...
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Tied-down occupation times of infinite ergodic transformations
We prove distributional limit theorems (conditional and integrated) for the occupation times of certain weakly mixing, pointwise dual ergodic...
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Uniform Convergence on Subspaces in the von Neumann Ergodic Theorem with Discrete Time
AbstractWe consider the power-law uniform (in the operator norm) convergence on vector subspaces with their own norms in the von Neumann ergodic...
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On spectral measures and convergence rates in von Neumann’s Ergodic theorem
We show that the power-law decay exponents in von Neumann’s Ergodic Theorem (for discrete systems) are the pointwise scaling exponents of a spectral...
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Ergodic theory of affine isometric actions on Hilbert spaces
The classical Gaussian functor associates to every orthogonal representation of a locally compact group G a probability measure preserving action of G ...
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Concepts of almost periodicity and ergodic theorems in locally convex spaces
We wish to investigate mean ergodic theorems for generalizations of almost periodic functions on semigroups, as well as for semigroups of operators...
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Contributions to the ergodic theory of hyperbolic flows: unique ergodicity for quasi-invariant measures and equilibrium states for the time-one map
We consider the horocyclic flow corresponding to a (topologically mixing) Anosov flow or diffeomorphism, and establish the uniqueness of transverse...
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Invariant Measures for Discontinuous Skew-Product Actions of Amenable Semigroups and Some Ergodic Results
In this paper, for skew-product actions (SPAs) of amenable semigroups (and commutative semigroups) with discontinuity from the point of view of...
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Invariant and Ergodic Probability Measures
The chapter starts with a detailed exposition on weak convergence and tightness. Then the class of invariant probability measures is defined and it...
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Stationary Processes and Ergodic Theory
Stationarity and invariance, two-sided extension, invariance and almost invariance, ergodicity, maximal ergodic lemma, discrete and continuoustime...
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Probability and Moment Inequalities for Additive Functionals of Geometrically Ergodic Markov Chains
In this paper, we establish moment and Bernstein-type inequalities for additive functionals of geometrically ergodic Markov chains. These...
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Exponent of Convergence of a Sequence of Ergodic Averages
AbstractFor a sequence of ergodic averages, we consider its exponent of convergence, which is a numerical characteristic of two-sided power-law...
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On Ergodic States, Spontaneous Symmetry Breaking and Quasi-Averages
It is shown that the Bogoliubov quasi-averages select the pure or ergodic states in the ergodic decomposition of the thermal (Gibbs) state. Our...
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Self-Joinings and Generic Extensions of Ergodic Systems
AbstractIt is proved that the generic extensions of a dynamical system inherit the triviality of pairwise independent self-joinings. This property...
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The Ergodic Theorem
If X n = ξ 1 ξ 2⋯ξ n is a transient random walk on a finitely generated group Γ with step distribution μ, then the probability q that it will never...