منابع مشابه
Subsequences of Sequences of Random Variables
Chatterji [2] has formulated the following heuristic principle: given any limit property for independent identically distributed random variables (i.i.d.r.v.'s), there exists an analogous property such that an arbitrary sequence of r.v.'s always has some subsequence possessing this analogous property. By 'arbitrary', we mean that no assumption concerning dependence is made, though it may be nec...
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By a classical result of Philipp (1977), for any positive sequence (nk)k≥1 satisfying the Hadamard gap condition, the discrepancy of (nkx)1≤k≤N mod 1 satisfies the law of the iterated logarithm. For sequences (nk)k≥1 growing subexponentially this result becomes generally false and the asymptotic behavior of the discrepancy remains unknown. In this paper we show that for randomly sampled subsequ...
متن کاملDescending subsequences of random permutations
Given a random permutation of the numbers 1, 2, . . . . n, let L, be the length of the longest descending subsequence of this permutation. Let F, be the minimal header (first element) of the descending subsequences having maximal length. It is known that EL,/&,,,, c and that c=2. However, the proofs that r=2 are far from elementary and involve limit processes. Several relationships between thes...
متن کاملEntropy conditions for subsequences of random variables with applications to empirical processes
We introduce new entropy concepts measuring the size of a given class of increasing sequences of positive integers. Under the assumption that the entropy function of A is not too large, many strong limit theorems will continue to hold uniformly over all sequences in A. We demonstrate this fact by extending the Chung-Smirnov law of the iterated logarithm on empirical distribution functions for i...
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The ratio of independent random variables arises in many applied problems. In this article, the distribution of the ratio X/Y is studied, when X and Y are independent Rice random variables. Ratios of such random variable have extensive applications in the analysis of noises of communication systems. The exact forms of probability density function (PDF), cumulative distribution function (CDF) a...
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ژورنال
عنوان ژورنال: Rocky Mountain Journal of Mathematics
سال: 1987
ISSN: 0035-7596
DOI: 10.1216/rmj-1987-17-1-115