The Law of the Iterated Logarithm for $B$-Valued Random Variables with Multidimensional Indices
نویسندگان
چکیده
منابع مشابه
On the law of the iterated logarithm for the discrepancy of sequences 〈nkx〉 with multidimensional indices
By a classical result of Weyl (1916), for any increasing sequence (nk) of positive integers, (nkx) is uniformly distributed mod 1 for almost all x. The precise asymptotics of the discrepancy of this sequence is known only in a few cases, e.g. for nk = k (Khinchin (1924)) and for lacunary (nk) (Philipp (1975)). In this paper we extend Philipp’s result to lacunary sequences with multidimensional ...
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ژورنال
عنوان ژورنال: The Annals of Probability
سال: 1989
ISSN: 0091-1798
DOI: 10.1214/aop/1176991425