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# 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 ...

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

Abstract. The well-known problem of least squares prediction of the stationary stochastic process x (t) is the problem of finding the functional x(τ) of the values x (f), t ≦ 0, which is the least squares approximation of the “future” value of the process x (τ), τ > 0.

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

between x (τ) and $$\tilde{x}\left( \tau \right)$$ [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 $$\tilde{x}\left( \tau \right)$$ 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 ...

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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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### Strong mixing conditions - Encyclopedia of Mathematics

2016-4-4  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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### 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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### 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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### 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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### 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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### 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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### A Gaussian mixture autoregressive model for univariate ...

2019-12-19  distribution is a Gaussian mixture with time varying mixing weights that depend on p laggedvaluesof theseriesinawaythathasanatural interpretation. Thus, similarlytothe linear Gaussian AR process, and contrary to (at least most) other nonlinear AR models, the structure of stationary marginal distributions of order p+1 or smaller is fully known.

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### On the Number of Modes of a Gaussian Mixture

2003-3-18  each component for m = 1;:::;M 1 is a Gaussian of mixing proportion ˇm and variance ˙2 m ˙2 M, and component M is a delta function of mixing proportion ˇM. Thus, p0 is a mixture of a delta and a GM with M 1 components. By the induction hypothesis the latter has M 1 modes at most, so p0 has M modes at most. Now apply Gaussian blurring to p0 ...

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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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### Lecture 13 Time Series: Stationarity, AR(p) MA(q)

2018-11-27  A: We need to impose conditions on ρk. Conditions weaker than "they are all zero;" but, strong enough to exclude the sequence of identical copies. Time Series – Ergodicity of the Mean • Definition: A covariance-stationary process is ergodic for the mean if plimz E(Zt) Ergodicity Theorem: Then, a sufficient condition for ergodicity for

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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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### 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 strong approximation for the empirical process of ...

2017-1-21  On strong approximation for the empirical process of stationary sequences. J´erˆome Dedecker a, Florence Merlevede b and Emmanuel Rio c. a Universit´e Paris Descartes, Laboratoire MAP5, UMR 8145 CNRS, 45 rue des Saints-Peres, F-75270 Paris cedex 06, France. E-mail: [email protected]

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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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### Mixing - Properties and Examples Paul Doukhan Springer

Mixing is concerned with the analysis of dependence between sigma-fields defined on the same underlying probability space. It provides an important tool of analysis for random fields, Markov processes, central limit theorems as well as being a topic of current research interest in its own right.

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