scholarly journals Quantum central limit theorems for weakly dependent maps I

1994 ◽  
Vol 63 (2) ◽  
pp. 183-212 ◽  
Author(s):  
L. Accardi ◽  
Y. G. Lu
Keyword(s):  
Central Limit ◽  
Limit Theorems ◽  
Central Limit Theorems ◽  
Weakly Dependent

ALMOST SURE CENTRAL LIMIT THEOREMS OF THE PARTIAL SUMS AND MAXIMA FROM COMPLETE AND INCOMPLETE SAMPLES OF STATIONARY SEQUENCES

2012 ◽  
Vol 12 (03) ◽  
pp. 1150026 ◽  
Author(s):  
ZUOXIANG PENG ◽  
BIN TONG ◽  
SARALEES NADARAJAH
Keyword(s):  
Central Limit ◽  
Random Vector ◽  
Limit Theorems ◽  
Random Sequence ◽  
Random Variables ◽  
Central Limit Theorems ◽  
Partial Sums ◽  
Stationary Sequences ◽  
Vector Formula ◽  
Weakly Dependent

Let (Xn) denote an independent and identically distributed random sequence. Let [Formula: see text] and Mn = max {X1, …, Xn} be its partial sum and maximum. Suppose that some of the random variables of X1, X2,… can be observed and denote by [Formula: see text] the maximum of observed random variables from the set {X1, …, Xn}. In this paper, we consider the joint limiting distribution of [Formula: see text] and the almost sure central limit theorems related to the random vector [Formula: see text]. Furthermore, we extend related results to weakly dependent stationary Gaussian sequences.

scholarly journals Central limit theorems for the excursion set volumes of weakly dependent random fields

Bernoulli ◽  
2012 ◽  
Vol 18 (1) ◽  
pp. 100-118 ◽  
Author(s):  
Alexander Bulinski ◽  
Evgeny Spodarev ◽  
Florian Timmermann
Keyword(s):  
Central Limit ◽  
Random Fields ◽  
Limit Theorems ◽  
Central Limit Theorems ◽  
Excursion Set ◽  
Weakly Dependent

scholarly journals Pressure Function and Limit Theorems for Almost Anosov Flows

2021 ◽  
Vol 382 (1) ◽  
pp. 1-47
Author(s):  
Henk Bruin ◽  
Dalia Terhesiu ◽  
Mike Todd
Keyword(s):  
Thermodynamic Properties ◽  
Central Limit ◽  
Limit Theorems ◽  
Central Limit Theorems ◽  
Stable Laws ◽  
Analytic Framework ◽  
Pressure Function ◽  
Hyperbolic Flows ◽  
Anosov Flows ◽  
Almost Anosov

AbstractWe obtain limit theorems (Stable Laws and Central Limit Theorems, both standard and non-standard) and thermodynamic properties for a class of non-uniformly hyperbolic flows: almost Anosov flows, constructed here. The link between the pressure function and limit theorems is studied in an abstract functional analytic framework, which may be applicable to other classes of non-uniformly hyperbolic flows.

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