000097249 001__ 97249 000097249 005__ 20240319080945.0 000097249 0247_ $$2doi$$a10.1007/s10959-020-01050-9 000097249 0248_ $$2sideral$$a120974 000097249 037__ $$aART-2022-120974 000097249 041__ $$aeng 000097249 100__ $$0(orcid)0000-0001-8331-5160$$aAdell, J.A.$$uUniversidad de Zaragoza 000097249 245__ $$aProbabilistic Stirling Numbers of the Second Kind and Applications 000097249 260__ $$c2022 000097249 5060_ $$aAccess copy available to the general public$$fUnrestricted 000097249 5203_ $$aAssociated 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. 000097249 536__ $$9info:eu-repo/grantAgreement/ES/MCIU/PGC2018-097621-B-I00 000097249 540__ $$9info:eu-repo/semantics/openAccess$$aby$$uhttp://creativecommons.org/licenses/by/3.0/es/ 000097249 590__ $$a0.8$$b2022 000097249 591__ $$aSTATISTICS & PROBABILITY$$b105 / 125 = 0.84$$c2022$$dQ4$$eT3 000097249 594__ $$a1.4$$b2022 000097249 592__ $$a0.659$$b2022 000097249 593__ $$aMathematics (miscellaneous)$$c2022$$dQ2 000097249 593__ $$aStatistics, Probability and Uncertainty$$c2022$$dQ2 000097249 593__ $$aStatistics and Probability$$c2022$$dQ2 000097249 655_4 $$ainfo:eu-repo/semantics/article$$vinfo:eu-repo/semantics/publishedVersion 000097249 7102_ $$12007$$2265$$aUniversidad de Zaragoza$$bDpto. Métodos Estadísticos$$cÁrea Estadís. Investig. Opera. 000097249 773__ $$g35 (2022), 636–652$$pJ. theor. probab.$$tJOURNAL OF THEORETICAL PROBABILITY$$x0894-9840 000097249 8564_ $$s340072$$uhttps://zaguan.unizar.es/record/97249/files/texto_completo.pdf$$yVersión publicada 000097249 8564_ $$s18802$$uhttps://zaguan.unizar.es/record/97249/files/texto_completo.jpg?subformat=icon$$xicon$$yVersión publicada 000097249 909CO $$ooai:zaguan.unizar.es:97249$$particulos$$pdriver 000097249 951__ $$a2024-03-18-12:32:13 000097249 980__ $$aARTICLE