# on conditions of strong mixing of a gaussian stationary

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

2006-7-28  (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 Conditions of Strong Mixing of A Gaussian Stationary ...

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

Local polynomial fitting has many exciting statistical properties which where established under i.i.d. setting. However, the need for nonlinear time series modeling, constructing predictive intervals, understanding divergence of nonlinear time series requires the development of the theory of local polynomial fitting for dependent data.

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

On Strong Mixing Conditions for Stationary Gaussian Processes 发布：经管之家 分类：Gauss软件培训 搜索 关于本站 人大经济论坛-经管之家：分享大学、考研、论文、会计、留学、数据、经济学、金融学、管理学、统计学、博弈论、统计年鉴、行业分析包括 ...

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### A NOTE ON STRONG MIXING - Lehigh University

2020-3-12  stationary gaussian sequence is strong mixing if it has a continuous spectral density that is bounded awayfrom 0. Chanda and Withers have considered strong mixing properties of the processYn=

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

between x (τ) and $$\widetilde{x}(\tau )$$ [here and later we can consider without loss of generality only the processes x (t) with Ex (t) = 0].If the process x (t) is Gaussian, the least squares approximation $$\widetilde{x}(\tau )$$ is linear; therefore, we can say that the problem of linear least squares prediction of the stationary process x (t) is the wide sense version of the general ...

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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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### Strong mixing conditions - Encyclopedia of Mathematics

2016-4-4  Here are just a couple of comments: For stationary Gaussian sequences, the α - and ρ -mixing conditions are equivalent to each other, and the ϕ - and ψ -mixing conditions are each equivalent to m -dependence. If a stationary Gaussian sequence has a continuous positive spectral density function, then it is ρ -mixing.

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### On The Spectrum Of Stationary Gaussian Sequences ...

2006-7-17  A Maximum Principle for the Stability Analysis of Positive Bilinear Control Systems with Applications to Positive Linear Switched Systems Bifurcation of Relative Equilibria in Infinite-Dimensional Hamiltonian Systems

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

On Strong Mixing Conditions for Stationary Gaussian Processes 发布：经管之家 分类：Gauss软件培训 搜索 关于本站 人大经济论坛-经管之家：分享大学、考研、论文、会计、留学、数据、经济学、金融学、管理学、统计学、博弈论、统计年鉴、行业分析包括 ...

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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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### 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

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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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### A strong mixing condition for second-order stationary ...

[10] I. A. Ibragimov, On the spectrum of stationary Gaussian sequences satisfying the strong mixing condition, Theory Probab. Appl. 10 (1965), 85-106; 15 (1970), 24-37. [11] I. A. Ibragimov and V. N. Solev, A condition for the regularity of a Gaussian stationary process, Soviet Math. Dokl. 10 (1969), 371-375.

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### CENTRAL LIMIT THEOREM FOR STATIONARY

2018-10-20  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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### A NOTE ON WEAK CONVERGENCE OF MEAN RESIDUAL

2017-2-3  For a sequence of strictly stationary uniform or strong mixing we estimate the mean residual time of the marginal distribution from the first n observations. Under appropriate conditions it is own that the estimate converges weakly to a well-defined Gaussian process even when the

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### 1. STATIONARY GAUSSIAN PROCESSES - math.iisc.ernet

2014-4-7  1. STATIONARY GAUSSIAN PROCESSES Below T will denote Rd or Zd.What is special about these index sets is that they are (abelian) groups. If X =(Xt)t∈T is a stochastic process, then its translate Xτ is another stochastic process on T deﬁned as Xτ(t)=X(t−τ).The process X is called stationary (or translation invariant) if Xτ =d X for all τ∈T. Let X be a Gaussian process on T with mean ...

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### A Gaussian Mixture Autoregressive Model for Univariate ...

2014-12-16  In contrast, the conditional distribution given the past observations is a Gaussian mixture with time-varying mixing weights that depend on p lagged values of the series in a natural and parsimonious way. Because of the known stationary distribution, exact maximum likelihood estimation is feasible and one can assess the applicability of the ...

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### Lesson 4: Stationary stochastic processes

2014-2-14  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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### 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

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

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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### Asymptotic Distribution Of Sum And Maximum For

2006-11-2  The main result in Hsing (1995) is that for strong mixing sequences, such that Sn satisfies the central limit theorem, asymptotic independence of (Sn, Mn) ensues. Gaussian sequences have long been studied with regard to the asymptotic properties of extreme values. It is well known that for stationary Gaussian sequences 6 Xn > with E Xn = 0 and E Xn

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### A NOTE ON FIRST PASSAGE TIMES OF STATIONARY

2003-8-1  (1.1) for certain types of stationary strong mixing sequences. For more restric-tive classes of weakly dependent stationary sequences such as absolutely regular (or weak Bernoulli) sequences and functionals of Markov chains and of moving averages having C1 spectral density, (1.1) can be strengthened to a Blackwell

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### Approximation of stationary solutions of Gaussian driven ...

2021-6-10  Approximation of stationary solutions of Gaussian driven Stochastic Differential Equations Serge Cohen, Fabien Panloup ... respectively to some conditions on the local behavior and on the memory of the process. (H1) For every i∈ {1, ... ≥1is Gaussian, (∆ i n) is in fact strong mixing (see ...

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### Gaussian Random Processes I.A. Ibragimov Springer

The book deals mainly with three problems involving Gaussian stationary processes. The first problem consists of clarifying the conditions for mutual absolute continuity (equivalence) of probability distributions of a "random process segment" and of finding effective formulas for densities of the

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### On Modeling a Class of Weakly Stationary Processes

In this article, we show that a general class of weakly stationary time series can be modeled applying Gaussian subordinated processes. We show that, for any given weakly stationary time series (zt)z∈N with given equal one-dimensional marginal distribution, one can always construct a function f and a Gaussian process (Xt)t∈N such that f(Xt ...

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### ASYMPTOTIC PROPERTIES OF THE MAXIMUM IN A

2018-11-16  The conditions of both types are weaker in Theorem 2.1 than in [4]. It is natural to inquire whether the conditions of Theorem 2.1 might be further weakened. In particular, might the conditions (2.1) or (2.2) be replaced by the condition that (2.8) lim r(t) = 0. (-♦ CO For the case of stationary Gaussian sequences, a similar question was answered

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### Lesson 4: Stationary stochastic processes

2014-2-14  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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### Examples of Stationary Processes 1) Strong Sense White ...

2006-1-14  Claim: if ǫis a weakly stationary series then Xt= P∞ j=0 ρ jǫ t−jconverges (technically it con-verges in mean square) and is a second order stationary solution to the equation (1). If ǫis a strictly stationary process then under some weak assumptions about how heavy the tails of ǫare Xt= P∞ j=0 ρ jǫ t−jconverges almost

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