Convergence rates in the SLLN for some classes of dependent random fields

Abstract

Let { X n , n ∈ N r } be a random field i.e. a family of random variables indexed by N r , r ⩾ 2 . We discuss complete convergence and convergence rates under assumption on dependence structure of random fields in the case of nonidentical distributions. Results are obtained for negatively associated random fields, ρ ⁎ -mixing random fields (having maximal coefficient of correlation strictly smaller then 1) and martingale random fields.