Probabilistic Stirling Numbers of the Second Kind and Applications

José A. Adell ()
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José A. Adell: Universidad de Zaragoza

Journal of Theoretical Probability, 2022, vol. 35, issue 1, 636-652

Abstract: 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.

Keywords: Probabilistic Stirling number; Moment; Edgeworth expansion; Lévy process; Cumulant; Generalized difference; 60E05; 05A19 (search for similar items in EconPapers)
Date: 2022
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DOI: 10.1007/s10959-020-01050-9

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