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

2011/07/19 by Richard C. Bradley, Bradley, Richard C.
Decision Sciences · Mathematics · #60G10 #60G60 #FOS: Mathematics #Probability (math.PR) #Probability and Risk Models #Stochastic processes and statistical mechanics #math.PR #msc:60G10 #msc:60G60

paper · pdf · doi:10.48550/arxiv.1107.3854

16 pages

arxiv created 2011/07/19 · openalex publication_date 2011/07/19 · arxiv updated 2011/07/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

For a given pair of positive integers d and N with N ≥ 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 ρ-, ρ'-, and ρ^*-mixing conditions can decay together at an arbitrary rate. Another, closely related result is also established. In particular, these constructions 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.

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