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Probabilistic Stirling Numbers of the Second Kind and Applications

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  • José A. Adell

    (Universidad de Zaragoza)

Abstract

Associated with each complex-valued random variable satisfying appropriate integrability conditions, we introduce a different generalization of the Stirling numbers of the second kind. Various equivalent definitions are provided. Attention, however, is focused on applications. Indeed, such numbers describe the moments of sums of i.i.d. random variables, determining their precise asymptotic behavior without making use of the central limit theorem. Such numbers also allow us to obtain explicit and simple Edgeworth expansions. Applications to Lévy processes and cumulants are discussed, as well.

Suggested Citation

  • José A. Adell, 2022. "Probabilistic Stirling Numbers of the Second Kind and Applications," Journal of Theoretical Probability, Springer, vol. 35(1), pages 636-652, March.
    • Handle: RePEc:spr:jotpro:v:35:y:2022:i:1:d:10.1007_s10959-020-01050-9
    DOI: 10.1007/s10959-020-01050-9
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    References listed on IDEAS

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    1. José Antonio Adell & Alberto Lekuona, 2007. "Berry–Esseen Bounds for Standardized Subordinators via Moduli of Smoothness," Journal of Theoretical Probability, Springer, vol. 20(2), pages 221-235, June.
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