Results 21 to 30 of about 23,064 (196)
Norm convergence of nilpotent ergodic averages [PDF]
, 2011 We show that multiple polynomial ergodic averages arising from nilpotent groups of measure preserving transformations of a probability space always converge in the L^2 norm.Comment: 17 pages.
Walsh, Miguel N.
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Convergence of diagonal ergodic averages [PDF]
Ergodic Theory and Dynamical Systems, 2009 AbstractTao has recently proved that ifT1,…,Tlare commuting, invertible, measure-preserving transformations on a dynamical system, then for anyL∞functionsf1,…,fl, the average (1/N)∑n=0N−1∏i≤lfi∘Tinconverges in theL2norm. Tao’s proof is unusual in that it translates the problem into a more complicated statement about the combinatorics of finite spaces ...
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Hierarchy of climate and hydrological uncertainties in transient low-flow projections [PDF]
Hydrology and Earth System Sciences, 2016 This paper proposes a methodology for estimating the transient probability distribution of yearly hydrological variables conditional to an ensemble of projections built from multiple general circulation models (GCMs), multiple statistical downscaling ...
J.-P. Vidal +4 more
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, 2023 We consider weighted ergodic averages indexed by primes, where the weight depends on the prime, and is a "trace function" coming from algebraic geometry. We obtain extensions the classical mean-ergodic and pointwise ergodic theorems, as well as some result in the topological setting, and raise some further problems.
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A method for visualization of invariant sets of dynamical systems based on the ergodic partition [PDF]
, 1999 We provide an algorithm for visualization of invariant sets of dynamical systems with a smooth invariant measure. The algorithm is based on a constructive proof of the ergodic partition theorem for automorphisms of compact metric spaces.
Mezić, Igor, Wiggins, Stephen
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(Uniform) convergence of twisted ergodic averages [PDF]
Ergodic Theory and Dynamical Systems, 2015 Let$T$be an ergodic measure-preserving transformation on a non-atomic probability space$(X,\unicode[STIX]{x1D6F4},\unicode[STIX]{x1D707})$. We prove uniform extensions of the Wiener–Wintner theorem in two settings: for averages involving weights coming from Hardy field functions $p$,$$\begin{eqnarray}\displaystyle \bigg\{\frac{1}{N}\mathop{\sum }_{n ...
Eisner, T., Krause, B.
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An Approach of Randomness of a Sample Based on Its Weak Ergodic Limit
Journal of Probability and Statistics, 2017 For a Polish Sample Space with a Borel σ-field with a surjective measurable transformation, we define an equivalence relation on sample points according to their ergodic limiting averages.
Jaime A. Londoño
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A remark on weighted averages for superadditive processes
International Journal of Mathematics and Mathematical Sciences, 1991 A decompostion of a superadditive process into a difference of an additive and a positive purely superadditive process is obtained. This result is used to prove an ergodic theorem for weighted averages of superadditive processes.
Dogan Cömez
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Nonconventional ergodic averages and nilmanifolds [PDF]
Annals of Mathematics, 2005 The authors prove the following extension of Furstenberg's theorem [\textit{J. Furstenberg}, J. Anal. Math. 31, 204--256 (1977; Zbl 0347.28016)]: Let \(T\) be a measure-preserving invertible transformation on a probability space and \(f_1,\dots,f_k\) be bounded measurable functions.
Host, Bernard, Kra, Bryna
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Ergodic averages with generalized weights [PDF]
Studia Mathematica, 2006 Two types of weighted ergodic averages are studied. It is shown that if F = {Fn} is an admissible superadditive process relative to a measure preserving transformation, then a Wiener-Wintner type result holds forF. Using this result new good classes of weights generated by such processes are obtained.
Doğan Çömez, Semyon N. Litvinov
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