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 theory. For a discussion of central limit theorems and related results under these conditions, the reader is referred to Peligrad [60] or Iosifescu [50]. This survey will be divided into eight sections, as follows: 1. Measures of dependence 2. Five strong mixing conditions 3. Mixing conditions for two or more sequences 4. Mixing conditions for Markov chains 5. Mixing conditions for Gaussian sequences 6. Some other special examples 7. The behavior of the dependence coefficients 8. Approximation of mixing sequences by other random sequences.

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