On Powers of Stieltjes Moment Sequences, I

Christian Berg ()
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Christian Berg: University of Copenhagen

Journal of Theoretical Probability, 2005, vol. 18, issue 4, 871-889

Abstract: For a Bernstein function f the sequence s n =f(1)·...· f(n) is a Stieltjes moment sequence with the property that all powers s n c ,c>0 are again Stieltjes moment sequences. We prove that $$s_n^c$$ 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 $$(\rho_c)_{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

Keywords: Moment sequence; infinitely divisible distribution (search for similar items in EconPapers)
Date: 2005
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DOI: 10.1007/s10959-005-7530-6

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