scholarly journals Central limit theorems for arrays of decimated linear processes

2009 ◽  
Vol 119 (9) ◽  
pp. 3006-3041 ◽  
Author(s):  
F. Roueff ◽  
M.S. Taqqu
Keyword(s):  
Central Limit ◽  
Limit Theorems ◽  
Central Limit Theorems ◽  
Linear Processes

CENTRAL LIMIT THEOREMS FOR WEIGHTED SUMS OF LINEAR PROCESSES: LP -APPROXIMABILITY VERSUS BROWNIAN MOTION

2009 ◽  
Vol 25 (3) ◽  
pp. 748-763 ◽  
Author(s):  
Kairat T. Mynbaev
Keyword(s):  
Brownian Motion ◽  
Central Limit ◽  
Asymptotic Expansions ◽  
Limit Theorems ◽  
Stochastic Calculus ◽  
Central Limit Theorems ◽  
Weighted Sums ◽  
Linear Processes

Standardized slowly varying regressors are shown to be Lp-approximable. This fact allows us to provide alternative proofs of asymptotic expansions of nonstochastic quantities and central limit results due to P.C.B. Phillips, under a less stringent assumption on linear processes. The recourse to stochastic calculus related to Brownian motion can be completely dispensed with.

scholarly journals Central limit theorems for long range dependent spatial linear processes

Bernoulli ◽  
2016 ◽  
Vol 22 (1) ◽  
pp. 345-375 ◽  
Author(s):  
S.N. Lahiri ◽  
Peter M. Robinson
Keyword(s):  
Long Range ◽  
Central Limit ◽  
Limit Theorems ◽  
Central Limit Theorems ◽  
Linear Processes

Central limit theorems for nearly long range dependent subordinated linear processes

2020 ◽  
Vol 57 (2) ◽  
pp. 637-656
Author(s):  
Martin Wendler ◽  
Wei Biao Wu
Keyword(s):  
Long Range ◽  
Central Limit ◽  
Short Range ◽  
Limit Theorems ◽  
Central Limit Theorems ◽  
Partial Sums ◽  
Long Range Dependence ◽  
Stationary Sequences ◽  
Linear Processes ◽  
Arbitrary Power

AbstractThe limit behavior of partial sums for short range dependent stationary sequences (with summable autocovariances) and for long range dependent sequences (with autocovariances summing up to infinity) differs in various aspects. We prove central limit theorems for partial sums of subordinated linear processes of arbitrary power rank which are at the border of short and long range dependence.

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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