On mixing sequences of random variables

1958 ◽  
Vol 9 (3-4) ◽  
pp. 389-393 ◽  
Author(s):  
A. Rényi ◽  
P. Révész
Keyword(s):  
Random Variables ◽  
Mixing Sequences

Some preliminary results on conditionally ψ-mixing sequences of random variables

Stochastics ◽  
2014 ◽  
Vol 87 (2) ◽  
pp. 326-346
Author(s):  
Demei Yuan ◽  
Shunjing Li ◽  
Bao Tao
Keyword(s):  
Random Variables ◽  
Preliminary Results ◽  
Mixing Sequences

scholarly journals Limiting behavior of the perturbed empirical distribution functions evaluated at U-statistics for strongly mixing sequences of random variables

1997 ◽  
Vol 10 (1) ◽  
pp. 3-20 ◽  
Author(s):  
Shan Sun ◽  
Ching-Yuan Chiang
Keyword(s):  
Empirical Distribution Function ◽  
Empirical Distribution ◽  
Random Variables ◽  
Distribution Functions ◽  
Limiting Behavior ◽  
U Statistics ◽  
Strongly Mixing ◽  
Almost Sure Representation ◽  
Mixing Sequences ◽  
Empirical Distribution Functions

We prove the almost sure representation, a law of the iterated logarithm and an invariance principle for the statistic Fˆn(Un) for a class of strongly mixing sequences of random variables {Xi,i≥1}. Stationarity is not assumed. Here Fˆn is the perturbed empirical distribution function and Un is a U-statistic based on X1,…,Xn.

Mixing

2021 ◽  
pp. 290-312
Author(s):  
James Davidson
Keyword(s):  
Sufficient Conditions ◽  
Random Variables ◽  
Linear Processes ◽  
Mixing Sequences

The concepts of strong and uniform mixing are developed in the context of sequences of random variables. A set of important inequalities limiting the dependence of mixing sequences is proved. The case of linear processes is examined in depth including some well‐known counterexamples. Sufficient conditions are derived for strong and uniform mixing of linear processes.

Moment bounds for non-stationary dependent sequences

1994 ◽  
Vol 31 (3) ◽  
pp. 731-742 ◽  
Author(s):  
Tae Yoon Kim
Keyword(s):  
Random Variables ◽  
Partial Sums ◽  
Unified Approach ◽  
Dependent Random Variables ◽  
Combinatorial Argument ◽  
Stationarity Condition ◽  
Weakly Dependent Random Variables ◽  
Mixing Sequences ◽  
Moment Bounds ◽  
Weakly Dependent

We provide a unified approach for establishing even-moment bounds for partial sums for a class of weakly dependent random variables satisfying a stationarity condition. As applications, we discuss moment bounds for various types of mixing sequences. To obtain even-moment bounds, we use a ‘combinatorial argument' developed by Cox and Kim (1990).

scholarly journals A note on two measures of dependence and mixing sequences

1983 ◽  
Vol 15 (02) ◽  
pp. 461-464
Author(s):  
Magda Peligrad
Keyword(s):  
Invariance Principle ◽  
Random Variables ◽  
Time Process ◽  
Mixing Rate ◽  
Coefficient Of Correlation ◽  
Mixing Coefficient ◽  
Measures Of Dependence ◽  
Mixing Coefficients ◽  
Two Measures ◽  
Mixing Sequences

In this note we establish an inequality between the maximal coefficient of correlation and the φ -mixing coefficient which is symmetric in its arguments. Motivated by this inequality, we introduce a mixing coefficient which is the product of two φ -mixing coefficients. We also study an invariance principle under conditions imposed on this new mixing coefficient. As a consequence of this result it follows that the invariance principle holds when either the direct-time process or its time-reversed process is φ -mixing; when both processes are φ-mixing the invariance principle holds for sequences of L 2-integrable random variables under a mixing rate weaker than that used by Ibragimov.

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