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Joint stable attraction of two sums of products

โœ Scribed by Daren B.H. Cline

Publisher
Elsevier Science
Year
1988
Tongue
English
Weight
563 KB
Volume
25
Category
Article
ISSN
0047-259X

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Let Xi, i = 1, 2, . . ., be i.i.d. symmetric random variables in the domain of attraction of o symmetric stable distribution (J, with 0 < a < 2. Let Yj, i = 1, 2, ..., be ii.d. symmetric stable random variables with the common distribution a,. It is known that under certain condi-

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A sequence of independent, identically distributed random vectors \(X_{1}, X_{2}, \ldots\) is said to belong to the \(Q\)-normed domain of semi-stable attraction of a random vector \(Y\) if there exist diagonal matrices \(A_{n}\), constant vectors \(b_{n}\) and a sequence \(\left(k_{n}\right)_{n}\)

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Closed expressions are obtained for sums of products of Bernoulli numbers of the form ( 2n 2j 1 , ..., 2jN ) B 2j1 } } } B 2jN , where the summation is extended over all nonnegative integers j 1 , ..., j N with j 1 + j 2 + } } } + j N =n. Corresponding results are derived for Bernoulli polynomials,