Abstract: | 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). |