On possible mixing rates for some strong mixing conditions for N-tuplewise independent random fields

• Autores: Richard C. Bradley
• Localización: Houston journal of mathematics, ISSN 0362-1588, Vol. 38, Nº 3, 2012, págs. 815-832
• Idioma: inglés
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• Resumen

  • 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 d-dimensional integer lattice and satisfy N-tuplewise independence, the dependence coefficients associated with the ?-, ?-prime- and ?*-mixing conditions can decay together at an arbitrary rate. If also d is at least 2 then, together with N-tuplewise 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 N-variate) distributions.