Characterization of weak convergence of Birkhoff sums for Gibbs-Markov maps
, 2009 We investigate limit theorems for Birkhoff sums of locally H\"older functions under the iteration of Gibbs-Markov maps. Aaronson and Denker have given sufficient conditions to have limit theorems in this setting.
Gouezel, Sebastien
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Feasible Multivariate Nonparametric Estimation Using Weak Separability [PDF]
One of the main practical problems of nonparametric regression estimation is the curse of dimensionality. The curse of dimensionality arises because nonparametric regression estimates are dependent variable averages local to the point at which the ...
Joris Pinkse
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Limit theorems for weighted Bernoulli random fields under Hannan's condition
, 2015 Consider a Bernoulli random field satisfying the Hannan's condition. Recently, invariance principles for partial sums of random fields over rectangular index sets are established.
Klicnarová, Jana +2 more
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Invariance principles for linear processes with application to isotonic regression
, 2011 In this paper, we prove maximal inequalities and study the functional central limit theorem for the partial sums of linear processes generated by dependent innovations. Due to the general weights, these processes can exhibit long-range dependence and the
Dedecker, Jérôme +2 more
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Local limit theorems in free probability theory
, 2010 In this paper, we study the superconvergence phenomenon in the free central limit theorem for identically distributed, unbounded summands. We prove not only the uniform convergence of the densities to the semicircular density but also their $L^p ...
Wang, Jiun-Chau
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On the functional CLT for stationary Markov Chains started at a point
, 2016 We present a general functional central limit theorem started at a point also known under the name of quenched. As a consequence, we point out several new classes of stationary processes, defined via projection conditions, which satisfy this type of ...
Barrera, David +2 more
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An invariance principle for weakly dependent stationary general models
, 2007 The aim of this article is to refine a weak invariance principle for stationary sequences given by Doukhan & Louhichi (1999). Since our conditions are not causal our assumptions need to be stronger than the mixing and causal $\theta$-weak dependence ...
Doukhan, Paul, Wintenberger, Olivier
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Weak convergence of probability measures on product spaces with applications to sums of random vectors [PDF]
Weak convergence of probability measures on product spaces with applications to sums of random ...
Iglehart, D. L.
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Central Limit Theorem with Exchangeable Summands and Mixtures of Stable Laws as Limits
, 2012 The problem of convergence in law of normed sums of exchangeable random variables is examined. First, the problem is studied w.r.t. arrays of exchangeable random variables, and the special role played by mixtures of products of stable laws - as limits in
Fortini, Sandra +2 more
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Periodic Lorentz gas with small scatterers. [PDF]
Probab Theory Relat Fields, 2023 Bálint P, Bruin H, Terhesiu D.
europepmc +1 more source