On almost sure max-limit theorems of complete and incomplete samples from stationary sequences

2011 ◽  
Vol 27 (7) ◽  
pp. 1323-1332 ◽  
Author(s):  
Bin Tong ◽  
Zuo Xiang Peng
Keyword(s):  
Limit Theorems ◽  
Stationary Sequences

Almost sure limit theorems of extremes of complete and incomplete samples of stationary sequences

Extremes ◽  
2009 ◽  
Vol 13 (4) ◽  
pp. 463-480 ◽  
Author(s):  
Zuoxiang Peng ◽  
Zhichao Weng ◽  
Saralees Nadarajah
Keyword(s):  
Limit Theorems ◽  
Stationary Sequences ◽  
Almost Sure Limit Theorems

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.

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.

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