A new computationally simple, speedy and accurate method is proposed to construct first-passage-time probability density functions for Gauss–Markov processes through time-dependent boundaries, both for fixed and for random initial states. Some applications to Brownian motion and to the Brownian bridge are then provided together with a comparison with some computational results by Durbin and by Daniels. Various closed-form results are also obtained for classes of boundaries that are intimately related to certain symmetries of the processes considered.

A computational approach to first-passage-time problems for Gauss-Markov processes.

DI NARDO, Elvira;
2001

Abstract

A new computationally simple, speedy and accurate method is proposed to construct first-passage-time probability density functions for Gauss–Markov processes through time-dependent boundaries, both for fixed and for random initial states. Some applications to Brownian motion and to the Brownian bridge are then provided together with a comparison with some computational results by Durbin and by Daniels. Various closed-form results are also obtained for classes of boundaries that are intimately related to certain symmetries of the processes considered.
33
2
453
482
http://projecteuclid.org/DPubS?service=UI&version=1.0&verb=Display&handle=euclid.aap/999188324
Brownian bridge; varying boundaries; Daniels boundary; Volterra integral equations
E. DI NARDO; A.G. NOBILE A.G.; E. PIROZZI E.; L.M. RICCIARDI
File in questo prodotto:
File Dimensione Formato  
AdvApplProb.pdf

Accesso riservato

Descrizione: Articolo principale
Tipo di file: PDF EDITORIALE
Dimensione 359.81 kB
Formato Adobe PDF
359.81 kB Adobe PDF   Visualizza/Apri   Richiedi una copia

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/2318/1561358
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 78
  • ???jsp.display-item.citation.isi??? 80
social impact