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On Powers of Stieltjes Moment Sequences, I

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  • Christian Berg

    (University of Copenhagen)

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

Suggested Citation

  • Christian Berg, 2005. "On Powers of Stieltjes Moment Sequences, I," Journal of Theoretical Probability, Springer, vol. 18(4), pages 871-889, October.
    • Handle: RePEc:spr:jotpro:v:18:y:2005:i:4:d:10.1007_s10959-005-7530-6
    DOI: 10.1007/s10959-005-7530-6
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    Cited by:

    1. Gwo Dong Lin & Jordan Stoyanov, 2015. "Moment Determinacy of Powers and Products of Nonnegative Random Variables," Journal of Theoretical Probability, Springer, vol. 28(4), pages 1337-1353, December.
    2. Arista, Jonas & Rivero, Víctor, 2023. "Implicit renewal theory for exponential functionals of Lévy processes," Stochastic Processes and their Applications, Elsevier, vol. 163(C), pages 262-287.
    3. P. Patie & A. Vaidyanathan, 2022. "Non‐classical Tauberian and Abelian type criteria for the moment problem," Mathematische Nachrichten, Wiley Blackwell, vol. 295(5), pages 970-990, May.
    4. Javier Cárcamo, 2017. "Maps Preserving Moment Sequences," Journal of Theoretical Probability, Springer, vol. 30(1), pages 212-232, March.

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