Probabilistic Stirling Numbers of the Second Kind and Applications

Adell, J.A. (Universidad de Zaragoza)

Resumen: 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.

Idioma: Inglés

DOI: 10.1007/s10959-020-01050-9

Año: 2022

Publicado en: JOURNAL OF THEORETICAL PROBABILITY 35 (2022), 636–652
ISSN: 0894-9840

Factor impacto JCR: 0.8 (2022)

Categ. JCR: STATISTICS & PROBABILITY rank: 105 / 125 = 0.84 (2022) - Q4 - T3

Factor impacto CITESCORE: 1.4 - Mathematics (Q3) - Decision Sciences (Q3)

Factor impacto SCIMAGO: 0.659 - Mathematics (miscellaneous) (Q2) - Statistics, Probability and Uncertainty (Q2) - Statistics and Probability (Q2)

Financiación: info:eu-repo/grantAgreement/ES/MCIU/PGC2018-097621-B-I00

Tipo y forma: Article (Published version)

Área (Departamento): Área Estadís. Investig. Opera. (Dpto. Métodos Estadísticos)