### On Strong Mixing Conditions for Stationary Gaussian ...

Jul 28, 2006  (1970) On the Spectrum of Stationary Gaussian Sequences Satisfying the Strong Mixing Condition. II. Sufficient Conditions. Mixing Rate. Theory of Probability Its Applications 15:1, 23-36. Citation PDF (1018 KB)

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### On strong mixing conditions for stationary Gaussian ...

CiteSeerX - Scientific documents that cite the following paper: On strong mixing conditions for stationary Gaussian processes

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### On Strong Mixing Conditions for Stationary Gaussian ...

On Strong Mixing Conditions for Stationary Gaussian Processes @article{Kolmogorov1960OnSM, title={On Strong Mixing Conditions for Stationary Gaussian Processes}, author={A. Kolmogorov and Y. Rozanov}, journal={Theory of Probability and Its Applications}, year={1960}, volume={5}, pages={204-208} }

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### On Conditions of Strong Mixing of A Gaussian Stationary ...

10%  Rozanov Y.A. (1992) On Conditions of Strong Mixing of A Gaussian Stationary Process. In: Shiryayev A.N. (eds) Selected Works of A. N. Kolmogorov. Mathematics and Its Applications (Soviet Series), vol 26.

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### Stationary Gaussian Processes Satisfying the Strong Mixing ...

10%  Cite this chapter as: Yaglom A.M. (1965) Stationary Gaussian Processes Satisfying the Strong Mixing Condition and Best Predictable Functionals.

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### strong mixing conditions - Encyclopedia of Mathematics

Strong Mixing Conditions Richard C. Bradley ... structure — for example, Markov chains, Gaussian processes, or linear models, including ARMA (autoregressive – moving average) models. However, it became clear in the middle ... for strictly stationary sequences, the strong mixing (α-mixing) condi-

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### A NOTE ON STRONG MIXING - Lehigh University

discussed that under what conditions the strong mixing property holds for linear stochastic processes and in particular ARMA processes. Then an example of Non-Strong mixing Autoregressive Processes is ... is a stationary Gaussian (without being necessarily a linear process) then Rozanov [1967] has

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### Strong mixing conditions - Encyclopedia of Mathematics

Apr 04, 2016  The term "strong mixing conditions" (plural) can reasonably be thought of as referring to all conditions that are at least as strong as (i.e. that imply) $\alpha$-mixing. In the classical theory, five strong mixing conditions (again, plural) have emerged as the most prominent ones: $\alpha$-mixing itself and four others that will be defined here.

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### (PDF) Strong mixing coefficients for non-commutative ...

Bounds for non-commutative versions of two classical strong mix-ing coefficients for q-Gaussian processes are found in terms of the angle between the underlying Hilbert spaces.

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### Lesson 4: Stationary stochastic processes

de nition of strong stationarity, therefore, strong stationarity does not necessarily imply weak stationarity. For example, an iid process with standard Cauchy distribution is strictly stationary but not weak stationary because the second moment of the process is not nite. Umberto Triacca Lesson 4: Stationary stochastic processes

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### A Note on Strong-Mixing Gaussian Sequences

This note extends a theorem of Welsch (1971) on the joint asymptotic distribution of some order statistics of a strong-mixing, stationary, Gaussian sequence.

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### A Note on Strassen's Law for Stationary Gaussian Sequences

A NOTE ON STRASSENS LAW FOR STATIONARY GAUSSIAN SEQUENCES By CHANDRAKANT M. DEO University of Ottawa, Canada SUMMARY. It is shown that Strassen's law of iterated logarithm applies to strong-mixing stationary Gaussian sequences under conditions weaker than those obtained so far. We assume the framework and notation in Deo (1973). The question of

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### On Strong Mixing Conditions for Stationary Gaussian ...

On Strong Mixing Conditions for Stationary Gaussian Processes. ... 请问谁能帮助我下一下这篇论文：On Strong Mixing Conditions for Stationary Gaussian Processes

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### Basic Properties of Strong Mixing Conditions.

by the author on basic properties of strong mixing conditions. AMS 2000 subject classi cations: Primary 60G10. Keywords and phrases: strong mixing conditions, stationary sequences. Received April 2005. This is an update of, and a supplement to, the author’s earlier survey paper [18] on basic properties of strong mixing conditions.

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### CENTRAL LIMIT THEOREM FOR STATIONARY

called strong mixing wasproposed in [12] andamountedto (2.1) sup IP(BF)-P(B)P(F)l-0 BeQo,Fea5 as n-oo wherePis theprobability measureofthestationaryprocess. Thecon-dition has interest on its ownbut it wasoriginally proposedtogetherwith some additional moment conditions to get asymptotic normality for partial sumsof the randomvariables ofa ...

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### Short Range and Long Range Dependence

Since conditions 1. and 2. are satisﬁed by X k, the fact that the limiting distribution is non-Gaussian implies that fX kg and fY kg cannot be strongly mixing. In their paper Helson and Sarason [6] obtained a necessary and sufﬁcient condition for a Gaussian stationary sequence to be strongly mixing

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### 8. Compressing stationary ergodic sources

i: stationary zero-mean Gaussian process with autocovariance function Rn. 1 lim n→∞ i lim [ S t Q n + R 1 = t 0 ergodic S i weakly mixing n 0 →∞ R[n 0 mixing n]= ⇔{S i} ⇔{ } Intuitively speaking, an ergodic pro]= cess ⇔ can {ha} ve in nite memory in general, but the memory is weak. Indeed, we see that for a stationary Gaussian ...

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### Lesson 4: Stationary stochastic processes

de nition of strong stationarity, therefore, strong stationarity does not necessarily imply weak stationarity. For example, an iid process with standard Cauchy distribution is strictly stationary but not weak stationary because the second moment of the process is not nite. Umberto Triacca Lesson 4: Stationary stochastic processes

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### Some Limit Theorems for Random Functions. I Theory of ...

Jul 17, 2006  (1970) Occupation times of stationary gaussian processes. Journal of Applied Probability 7:03, 721-733. (1970) Occupation times of stationary gaussian processes. ... (1960) On Strong Mixing Conditions for Stationary Gaussian Processes. Theory of Probability Its Applications 5:2, 204-208. Abstract PDF (498 KB) ...

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### Short-range dependent processes subordinated to the ...

Mar 01, 2016  There are all kinds of weak dependence. For example, strong mixing. Short-range dependence (SRD) is also a form of weak dependence. It occurs in the c

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### A central limit theorem and strong mixing conditions (1956)

In this paper we study the central limit theorem and its weak invariance principle for sums of a stationary sequence of random variables, via a martingale decomposition. Our conditions involve the conditional expectation of sums of random variables with respect to the distant past. For the sake of applications, we also give su#cient conditions ...

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### Rational spectral densities and strong mixing Semantic ...

This article is concerned with stationary random fields with rational spectral densities. The dichotomy between the one-parameter and multiparameter cases is explored, particularly in terms of a strong mixing condition. The rich variety of behavior exhibited by the multiparameter case is demonstrated.

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### Maximal Inequalities and an Invariance Principle for a ...

The aim of this paper is to investigate the properties of the maximum of partial sums for a class of weakly dependent random variables which includes the instantaneous filters of a Gaussian sequence having a positive continuous spectral density. The results are used to obtain an invariance principle for strongly mixing sequences of random variables in the absence of stationarity or strong ...

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### Abstract STRONG AND UNIFORM MIXING; AUTOREGRESSIVE

is uniformly pure non-deterministic. He also gives equivalent conditions for strong mixing in terms of the transition operator and the invariant probability measure. Ibragimov and Linnik [10] established that a stationary gaussian sequence is strong mixing if it has a

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### Conditions for a Class of Stationary Gaussian Processes to ...

Necessary and sufficient conditions are given for a class of stationary Gaussian processes to be mixing in the sense of Kolmogorov.

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### On Strong Mixing Conditions for Stationary Gaussian ...

On Strong Mixing Conditions for Stationary Gaussian Processes. ... 请问谁能帮助我下一下这篇论文：On Strong Mixing Conditions for Stationary Gaussian Processes

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### A Note on Strassen's Law for Stationary Gaussian Sequences

A NOTE ON STRASSENS LAW FOR STATIONARY GAUSSIAN SEQUENCES By CHANDRAKANT M. DEO University of Ottawa, Canada SUMMARY. It is shown that Strassen's law of iterated logarithm applies to strong-mixing stationary Gaussian sequences under conditions weaker than those obtained so far. We assume the framework and notation in Deo (1973). The question of

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### On the rate of strong mixing in stationary Gaussian random ...

Rosenblatt showed that a stationary Gaussian random field is strongly mixing if it has a positive, continuous spectral density. In this article, spectral criteria are given for the rate of strong mixing in such a field. ... On a strong mixing condition for stationary Gaussian processes, Theory Probab. Appl. 5 (1960), 204-208.

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### A central limit theorem and strong mixing conditions (1956)

In this paper we study the central limit theorem and its weak invariance principle for sums of a stationary sequence of random variables, via a martingale decomposition. Our conditions involve the conditional expectation of sums of random variables with respect to the distant past. For the sake of applications, we also give su#cient conditions ...

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### Abstract STRONG AND UNIFORM MIXING; AUTOREGRESSIVE

is uniformly pure non-deterministic. He also gives equivalent conditions for strong mixing in terms of the transition operator and the invariant probability measure. Ibragimov and Linnik [10] established that a stationary gaussian sequence is strong mixing if it has a

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### Strong Gaussian approximations of product-limit and ...

Apr 01, 2010  Under strong mixing condition, the strong approximation of the normed quantile process ρ n (p) by a two parameter Gaussian process at the rate O ((log n) − λ) for some λ > 0, was obtained by Fotopoulos et al. (1994) and was later improved by Yu (1996).

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### conditions

weaker distributional mixing conditions. Thus we need to impose extra condition to obtain a Poisson process in the limit. We now describe an application of Theorem 3.1 to a strictly stationary sequence {Zj: j≥ 1} under strong mixing conditions. There exist several coeﬃcients ’measuring’ the dependence between two σ-algebras A

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### Lecture 1: Stationary Time Series

Lecture 1: Stationary Time Series∗ 1 Introduction If a random variable X is indexed to time, usually denoted by t, the observations {X t,t ∈ T} is called a time series, where T is a time index set (for example, T = Z, the integer set).

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### ON THE DEPENDENCE COEFFICIENTS ASSOCIATED WITH

For this question for stationary Gaussian sequences, see e.g. [23]. For this question for ARMA processes, see e.g. [15]. Some information on this question for strictly stationary Markov chains and for stationary Gaussian sequences is also given in [7]. Of course most of the development of limit theory under strong mixing conditions in

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### AN APPLICATION THE CENTRAL LIMIT THEOREM

The strong mixing condition (1) is satisfied in the broad class of ergodic Markovprocessesandalso in Gaussianprocesses. In [12] it wasestablishedthat for a stationary Gaussian process the strong mixing property is associated with the smoothness of its spectral

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### 8. Compressing stationary ergodic sources

i: stationary zero-mean Gaussian process with autocovariance function Rn. 1 lim n→∞ i lim [ S t Q n + R 1 = t 0 ergodic S i weakly mixing n 0 →∞ R[n 0 mixing n]= ⇔{S i} ⇔{ } Intuitively speaking, an ergodic pro]= cess ⇔ can {ha} ve in nite memory in general, but the memory is weak. Indeed, we see that for a stationary Gaussian ...

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### Stationary process - Wikipedia

In mathematics and statistics, a stationary process (or a strict/strictly stationary process or strong/strongly stationary process) is a stochastic process whose unconditional joint probability distribution does not change when shifted in time. Consequently, parameters such as mean and variance also do not change over time. To get an intuition of stationarity, one can imagine a frictionless ...

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