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Submultiplicative moments of the supremum of a random walk with negative drift

โœ Scribed by M.S. Sgibnev

Publisher
Elsevier Science
Year
1997
Tongue
English
Weight
366 KB
Volume
32
Category
Article
ISSN
0167-7152

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โœฆ Synopsis

Let {Sn } be the sequence of partial sums of independent identically distributed random variables with negative mean. Necessary and sumcient conditions are obtained for Efp(M~ ) to be finite, where ~(x) is a non-decreasing submultiplicative function, i.e. ~p(x + y)<~cp(x)c~(y), and Moยข = sup{0, Si, $2 .... }. This generalizes a well-known result on moments of M~ proved by Kiefer and Wolfowitz (1956). Submultiplicative moments of the first positive sum are also considered.

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