On powers of Stieltjes moment sequences, I
نویسنده
چکیده
For a Bernstein function f the sequence sn = f(1)·. . .·f(n) is a Stieltjes moment sequence with the property that all powers sn, c > 0 are again Stieltjes moment sequences. We prove that sn is Stieltjes determinate for c ≤ 2, but it can be indeterminate for c > 2 as is shown by the moment sequence (n!)c, corresponding to the Bernstein function f(s) = s. Nevertheless there always exists a unique product convolution semigroup (ρc)c>0 such that ρc has moments sn. We apply the indeterminacy of (n!) c for c > 2 to prove that the distribution of the product of p independent identically distributed normal random variables is indeterminate if and only if p ≥ 3. 2000 Mathematics Subject Classification: primary 44A60; secondary 60E07.
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