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.
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Research supported by National Natural Science Foundation of China (197010011).
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Lixin, Z., Xiuyun, W. Convergence rates in the strong laws of asymptotically negatively associated random fields. Appl. Math. Chin. Univ. 14, 406–416 (1999). https://doi.org/10.1007/s11766-999-0070-6
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DOI: https://doi.org/10.1007/s11766-999-0070-6