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

Jul 28, 2006  (2020) Mixing and moments properties of a non-stationary copula-based Markov process. Communications in Statistics - Theory and Methods 49 :18, 4559-4570. (2020) Semiparametric estimation with spatially correlated recurrent events.

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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 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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### A NOTE ON STRONG MIXING - Lehigh University

and in particular ARMA processes. Then an example of Non-Strong mixing Autoregressive Processes is discussed here. Keywords: Harris Chain, Stationary Processes, Strong Mixing, ARMA Processes 1 Introduction In order to be able to state our results precisely, let us start with a review of mixing conditions. Let {X tm n =σ{X t: n≤ t≤ m}

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### Strong mixing conditions - Encyclopedia of Mathematics

Apr 04, 2016  Strong Mixing Conditions. Richard C. Bradley Department of Mathematics, Indiana University, Bloomington, Indiana, USA There has been much research on stochastic models that have a well defined, specific structure --- for example, Markov chains, Gaussian processes, or linear models, including ARMA (autoregressive -- moving average) models.

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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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### (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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### 1. STATIONARY GAUSSIAN PROCESSES

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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### Short Range and Long Range Dependence

strong mixing for stationary Gaussian sequences. In Sect.3 I will give a discussion of processes subordinated to Gaussian processes and in Sect.4 results concerning the ﬁnite Fourier transform is noted. In Sect.5 a number of open questions are considered. In an effort to obtain a central limit theorem for a dependent sequence of random

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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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### [PDF] Central limit theorem for stationary processes ...

ROZANOV , " On strong mixing conditions for stationary Gaussian processes , " Theory Prob The existence of stationary measures for certain Markov processes , ' Proceedings of the Third Berkeley Symposium on Mathematical Statistics and Probability

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### Nonparametric estimation of conditional probability ...

Jun 01, 1989  A.N. Kolmogorov and Yu.A. Rozanov, On strong mixing conditions for stationary Gaussian processes, Theory Probability Appl. 5 (1960) 204-207. [3] E. Masry, Almost sure convergence of recursive density estimators for stationary mixing processes

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

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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### Lesson 4: Stationary stochastic processes

Weakly stationary stochastic processes Thus a stochastic process is covariance-stationary if 1 it has the same mean value, , at all time points; 2 it has the same variance, 0, at all time points; and 3 the covariance between the values at any two time points, t;t k,

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### ρ -混合序列完全矩收敛的精确渐近性

[1] KOLMOGOROV A N, ROZANOV Y A. On strong mixing conditions for stationary gaussian processes[J]. Theory of Probability Its Applications, 1960, 5(2):204-208. [2] 姜德元. 关于ρ-混合序列对数律的收敛速度[J]. 应用数学,2002,15(3):32-37. JIANG Deyuan. On the convergence rates in the law of iterated logarithm of ρ-mixing ...

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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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### Murray Rosenblatt’s Contributions to Strong Mixing ...

Mar 24, 2011  Murray Rosenblatt’s research has contributed much to the field of “strong mixing conditions,” (i) by providing many results of his own in that field, and (ii) by inspiring a vast amount of research in that field by other people. This note will give just a

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

A theorem is proved in § 3 on the convergence of the distribution of the number of intersections of a high level to a Poisson distribution for stationary Gaussian processes, which satisfy the “strong mixing condition”. Some conditions under which stationary processes possess strong mixing are given in §4.

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### cambridge

Adv. Appl. Prob. 31, 158–177 (1999) Printed in Northern Ireland Applied Probability Trust 1999 CENTRAL LIMIT THEOREM FOR WAVE-FUNCTIONALS OF GAUSSIAN PROCESSES

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

On Strong Mixing Conditions for Stationary Gaussian Processes-经管之家官网！ ... 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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### AMS :: Proceedings of the American Mathematical Society

Introduction to strong mixing conditions. Technical report, Indiana University, Bloomington, 2002. ISBN 1-58902-566-0. ... On a strong mixing condition for stationary Gaussian processes, Teor. Verojatnost. i Primenen. 5 (1960), 222–227 (Russian, with English summary). MR 0133175; Edward Nelson. Notes on non-commutative integration.

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

A theorem is proved in § 3 on the convergence of the distribution of the number of intersections of a high level to a Poisson distribution for stationary Gaussian processes, which satisfy the “strong mixing condition”. Some conditions under which stationary processes possess strong mixing are given in §4.

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### Richard C. Bradley, Mixing Conditions

3. Five classic strong mixing conditions 4. Norms and connections with interpolation theory 5. Some other strong mixing conditions 6.Independent pairs of 6-fields 7. Markov chains 8. Second order properties 9. Stationary Gaussian sequences 10. Central limit theorems under the strong mixing

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### ERGODIC PROPERTIES OF STATIONARY STABLE PROCESSES

conditions for stationary SaS processes to be metrically transitive (Theorem 1) and mixing (Theorem 2). We then consider some important special classes of stationary SaS processes. We show that sub-Gaussian stationary processes are never metrically transitive (Theorem 3).

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### Nonparametric estimation of conditional probability ...

Jun 01, 1989  A.N. Kolmogorov and Yu.A. Rozanov, On strong mixing conditions for stationary Gaussian processes, Theory Probability Appl. 5 (1960) 204-207. [3] E. Masry, Almost sure convergence of recursive density estimators for stationary mixing processes

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### On the ergodicity and mixing of maxŒstable processes

ity and mixing conditions given in Section 3.2 are easy to verify for large classes of processes. The moving maxima or more generally the mixed moving maxima processes in (1.2) (1.3), for example, are always mixing. We discuss an example of a ’doubly stochastic’ stationary Frechet process, intro-

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### Precise asymptotics of complete moment convergence for ρ ...

[1] KOLMOGOROV A N, ROZANOV Y A. On strong mixing conditions for stationary gaussian processes[J]. Theory of Probability Its Applications, 1960, 5(2):204-208. [2] 姜德元. 关于ρ-混合序列对数律的收敛速度[J]. 应用数学,2002,15(3):32-37. JIANG Deyuan. On the convergence rates in the law of iterated logarithm of ρ-mixing ...

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### ρ -混合序列完全矩收敛的精确渐近性

[1] KOLMOGOROV A N, ROZANOV Y A. On strong mixing conditions for stationary gaussian processes[J]. Theory of Probability Its Applications, 1960, 5(2):204-208. [2] 姜德元. 关于ρ-混合序列对数律的收敛速度[J]. 应用数学,2002,15(3):32-37. JIANG Deyuan. On the convergence rates in the law of iterated logarithm of ρ-mixing ...

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### Strong Mixing Condition (数学者の一人ぐらし)

Kolmogorov,A.N. and Rozanov,Yu.A. On Strong Mixing Conditions for Stationary Gaussian Processes, Theory of Probability and its Applicatins,vol.V no.2(1960)204-208. Rosenblatt M. A central limit theoem and a strong mixing condition, Proc.Nat.Acad.Sci.Wash.,42,1(1956) Eric Hayashi ,The spectal density of a strong mixing stationary Gaussian process,

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### A Note on the Almost Sure Central Limit Theorem for ...

Kolmogorov, A.N. and Rozanov, U.A. (1960) On Strong Mixing Conditions for Stationary Gaussian Processes. Theory of Probability and Its Applications, 5, 204-208. ... (1988) On Strong Versions of the Central Limit Theorem. ... I. and Csáki, E. (2001) A Universal Result in Almost Sure Central Limit Theory. Stochastic Processes and Their ...

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### 14 RESEARCH NOTES

represented as a strictly stationary process with common mean and standard deviation σ. In this discussion, the variables in ... To show that -mixing holds in the limited normal case, choose , select a sequence ... and Y. A. Rozanov. 1960. “On Strong Mixing Conditions for Stationary Gaussian Processes.” Theory of Probability and Its ...

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### DISTRIBUTION OF THE SUPREMUM LOCATION OF STATIONARY PROCESSES

The location of the unique supremum of a stationary process on an interval does not need to be uniformly distributed over that interval. We describe all possible distributions of the supremum location for a broad class of such stationary processes.

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