A Remark on Baum-katz Type Theorem for Φ-mixing Sequences of Random Variables
نویسنده
چکیده
This notion was first introduced and discussed by Hsu and Robbins in [3]. They proved that the sequence of arithmetic means of independent, identically distributed (i.i.d.) random variables converges completely to the expected value of summands, provided the variance is finite. The result proved by Hsu and Robbins [3] was further generalized and extended by many authors (see e.g. [1, 2, 4]). Katz [4], Baum and Katz [1] formed the following generalization, with a normalization of MarcinkiewiczZygmund type (see [2]):
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