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Associated to each complex-valued random variable satisfying appropriateintegrability conditions, we introduce a different generalization of theStirling numbers of the second kind. Various equivalent definitions areprovided. Attention, however, is focused on applications. Indeed, such numbersdescribe the moments of sums of i.i.d. random variables, determining theirprecise asymptotic behavior without making use of the central limit theorem.Such numbers also allow us to obtain explicit and simple Edgeworth expansions.Applications to L\'{e}vy processes and cumulants are discussed, as well.

Probabilistic Stirling numbers of the second kind and applications