Convergence rates in the strong laws of asymptotically negatively associated random fields

In this paper, a notion of negative side ϱ-mixing (ϱ ⁻-mixing) which can be regarded as asymptotic negative association is defined, and some Rosenthal type inequalities for ϱ ⁻-mixing random fields are established. The complete convergence and almost sure summability on the convergence rates with respect to the strong law of large numbers are also discussed for ϱ ⁻-mixing random fields. The results obtained extend those for negatively associated sequences and ϱ ^* random fields. Research supported by National Natural Science Foundation of China (197010011).