Abstract
AbstractAssociated 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.
Funder
Ministerio de Ciencia, Innovación y Universidades
Publisher
Springer Science and Business Media LLC
Subject
Statistics, Probability and Uncertainty,General Mathematics,Statistics and Probability
Reference20 articles.
1. Abramowitz, M., Stegun, I.A.: Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables. Dover, New York (1992)
2. Adell, J.A., Lekuona, A.: Berry-Esseen bounds for standardized subordinators via moduli of smoothness. J. Theor. Probab. 20, 221–235 (2007)
3. Adell, J.A., Lekuona, A.: A probabilistic generalization of the Stirling numbers of the second kind. J. Number Theory 194, 335–355 (2019)
4. Adell, J.A., Lekuona, A.: A unified approach to higher order convolutions within a certain subset of Appell polynomials, Mediterr. J. Math. 17(2), Art. 63, 17 pp (2020)
5. Barbour, A.D.: Asymptotic expansions based on smooth functions in the central limit theorem. Probab. Theory Related Fields 72, 289–303 (1986)
Cited by
2 articles.
订阅此论文施引文献
订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献