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}
}
  • R. C. Bradley
  • Published 21 April 2005
  • Mathematics
  • Probability Surveys
This is an update of, and a supplement to, a 1986 survey paper by the author on basic properties of strong mixing conditions. 

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References

SHOWING 1-10 OF 168 REFERENCES

A caution on mixing conditions for random fields

On the Central Limit Theorem for Stationary Mixing Random Fields

A simple proof of a central limit theorem for stationary random fields under mixing conditions is given, generalizing some results obtained by more complicated methods, e.g. Bernstein's method.

The central limit theorem for Tukey's 3R smoother

Identical mixing rates

SummaryFor strictly stationary sequences, Ψ-mixing at a given mixing rate satisfying a log-convexity condition, does not imply α-mixing at any essentially faster rate.

Basic Properties of Strong Mixing Conditions

This is a survey of the basic properties of strong mixing conditions for sequences of random variables. The focus will be on the “structural” properties of these conditions, and not at all on limit

The functional central limit theorem under the strong mixing condition

We prove a central limit theorem for strongly mixing sequences under a sharp sufficient condition which combines the rate of the strong mixing coefficient with the quantile function. The result

Remarks on the Foundations of Measures of Dependence.

Abstract : This paper is a study of several aspects of measures of dependence, the various comparisons between them, and their foundation as norms of the bilinear form covariance. Additional

The invariance principle for ϕ-mixing sequences

SummaryIn this paper we investigate the invariance principle for ϕ-mixing sequences, satisfying restrictions on the variances which are a weak form of stationarity. No mixing rate is assumed. For

Invariance principles under a two-part mixing assumption

...