Results 1 
2 of
2
Basic Properties of Strong Mixing Conditions. A Survey and Some Open Questions
 PROBABILITY SURVEYS
, 2005
"... This is an update of, and a supplement to, the author’s earlier survey paper [18] on basic properties of strong mixing conditions. That paper appeared in 1986 in a book containing survey papers on various types of dependence conditions and the limit theory under them. The survey here will include pa ..."
Abstract

Cited by 121 (0 self)
 Add to MetaCart
(Show Context)
This is an update of, and a supplement to, the author’s earlier survey paper [18] on basic properties of strong mixing conditions. That paper appeared in 1986 in a book containing survey papers on various types of dependence conditions and the limit theory under them. The survey here will include part (but not all) of the material in [18], and will also describe some relevant material that was not in that paper, especially some new discoveries and developments that have occurred since that paper was published. (Much of the new material described here involves “interlaced ” strong mixing conditions, in which the index sets are not restricted to “past ” and “future.”) At various places in this survey, open problems will be posed. There is a large literature on basic properties of strong mixing conditions. A survey such as this cannot do full justice to it. Here are a few references on important topics not covered in this survey. For the approximation of mixing sequences by martingale differences, see e.g. the book by Hall and Heyde [80]. For the direct approximation of mixing random variables by independent ones,
ON POSSIBLE MIXING RATES FOR SOME STRONG MIXING CONDITIONS FOR NTUPLEWISE INDEPENDENT RANDOM FIELDS
"... Abstract. For a given pair of positive integers d and N with N at least 2, for strictly stationary random fields that are indexed by the ddimensional integer lattice and satisfy Ntuplewise independence, the dependence coefficients associated with the rho, rhoprime and rhostarmixing condition ..."
Abstract
 Add to MetaCart
(Show Context)
Abstract. For a given pair of positive integers d and N with N at least 2, for strictly stationary random fields that are indexed by the ddimensional integer lattice and satisfy Ntuplewise independence, the dependence coefficients associated with the rho, rhoprime and rhostarmixing conditions can decay together at an arbitrary rate. If also d is at least 2 then, together with Ntuplewise independence, the first two mixing conditions can hold with the same arbitrary rate of decay while the third fails to hold. The proofs of these results provide classes of examples pertinent to limit theory for random fields that involve such mixing conditions together with certain types of “extra ” assumptions on the marginal and bivariate (or Nvariate) distributions. 1.