# Basic properties of strong mixing conditions. A survey and some open questions

@article{Bradley2005BasicPO, title={Basic properties of strong mixing conditions. A survey and some open questions}, author={Richard C. Bradley}, journal={Probability Surveys}, year={2005}, volume={2}, pages={107-144} }

This is an update of, and a supplement to, a 1986 survey paper by the author on basic
properties of strong mixing conditions.

## 715 Citations

Mixing conditions of conjugate processes

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We give sufficient conditions ensuring that a $\psi$-mixing property holds for the sequence of empirical CDFs associated to a conjugate process.

A β-mixing inequality for point processes induced by their intensity functions

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We prove a general inequality on β-mixing coefficients of point processes depending uniquely on their n-th order intensity functions. We apply this inequality in the case of determinantal point…

Asymptotic behaviour of frequency polygons under φ-mixing samples

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ABSTRACT Under mild conditions, we study the asymptotic behaviour of the uniformly strong consistency of the frequency polygon investigated by Scott under φ −mixing samples. The results obtained…

Limit theorems for linear processes generated by ρ-mixing sequence

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An Inequality of the Bernstein-type for $\beta$-mixing Time Series

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In this article we present a Bernstein inequality for sums of random variables which are $\beta$-mixing. The inequality can be used to derive concentration inequalities. It can be useful to obtain…

Some mixing properties of conditionally independent processes

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ABSTRACT In this paper, we consider conditionally independent processes with respect to some dynamic factor. More precisely, we assume that for all n, random variables (Xi)i ⩽ n are conditionally…

A bound of the β-mixing coefficient for point processes in terms of their intensity functions

- MathematicsStatistics & Probability Letters
- 2019

Abstract We prove a general inequality on β -mixing coefficients of point processes depending uniquely on their n th order intensity functions. We apply this inequality in the case of determinantal…

A Bernstein Inequality For Spatial Lattice Processes

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In this article we present a Bernstein inequality for sums of random variables which are defined on a spatial lattice structure. The inequality can be used to derive concentration inequalities. It…

Strong Approximation for Mixing Sequences with Infinite Variance

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- 2006

In this paper we prove a strong approximation result for a mixing sequence with infinite variance and logarithmic decay rate of the mixing coefficient. The result is proved under the assumption that…

Consistency of the frequency polygon estimators of density mode for strongly mixing processes

- MathematicsCommunications in Statistics - Theory and Methods
- 2021

We consider a simple estimator of the density mode using the frequency polygon estimate. We investigate strong consistency of the estimator for strong mixing sequence of real variables under mild a...

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