Ricerche di Matematica

, Volume 68, Issue 2, pp 629–659 | Cite as

First-passage times and related moments for continuous-time birth–death chains

  • Virginia Giorno
  • Amelia G. NobileEmail author


First-passage time problems for continuous-time birth–death chains are considered. Recursive formulas for the moments of the first-exit time and of the first-passage time in terms of the potential coefficients are explicitly obtained. Making use of the probability current, some functional relations between transition probabilities for unrestricted and restricted continuous-time birth–death chains are determined. Finally, two continuous-time birth–death chains with constant rates are taken in account; for them, closed form results on the first-exit time and on the first-passage time are explicitly obtained.


First-passage time First-exit time Double-ended system Symmetric system 

Mathematics Subject Classification

60J27 60J80 



This work has been performed under partial support of the G.N.C.S.-INdAM.


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Copyright information

© Università degli Studi di Napoli "Federico II" 2018

Authors and Affiliations

  1. 1.Dipartimento di InformaticaUniversità degli Studi di SalernoFiscianoItaly

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