Random central limit theorems for linear processes with weakly dependent innovations

2012 ◽  
Vol 41 (3) ◽  
pp. 313-322 ◽  
Author(s):  
Eunju Hwang ◽  
Dong Wan Shin
Keyword(s):  
Central Limit ◽  
Limit Theorems ◽  
Central Limit Theorems ◽  
Linear Processes ◽  
Weakly Dependent

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.

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
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