On the Estimation of First-Passage Time Densities for a Class of Gauss-Markov Processes

  • A. G. Nobile
  • E. Pirozzi
  • L. M. Ricciardi
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4739)


For a class of Gauss-Markov processes the asymptotic behavior of the first passage time (FPT) probability density function (pdf) through certain time-varying boundaries is determined. Computational results for Wiener, Ornstein-Uhlenbeck and Brownian bridge processes are considered to show that the FPT pdf through certain large boundaries exhibits for large times an excellent asymptotic approximation.


Probability Density Function Large Time Passage Time Wiener Process Brownian Bridge 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Di Nardo, E., Nobile, A.G., Pirozzi, E., Ricciardi, L.M.: A computational approach to first-passage-time problems for Gauss-Markov processes. Adv. Appl. Prob. 33, 453–482 (2001)zbMATHCrossRefGoogle Scholar
  2. 2.
    Giorno, V., Nobile, A.G., Ricciardi, L.M.: On the asymptotic behaviour of first–passage–time densities for one–dimensional diffusion processes and varying boundaries. Adv. Appl. Prob. 22, 883–914 (1990)zbMATHCrossRefMathSciNetGoogle Scholar
  3. 3.
    Larson, H.J., Shubert, B.O.: Probabilistic models in engineering sciences. In: Random variables and stochastic processes, vol. 1, John Wiley & Sons, New York (1979)Google Scholar
  4. 4.
    Nobile, A.G., Ricciardi, L.M., Sacerdote, L.: Exponential trends of Ornstein-Uhlenbeck first-passage-time densities. J. Appl. Prob. 22, 360–369 (1985)zbMATHCrossRefMathSciNetGoogle Scholar
  5. 5.
    Ricciardi, L.M., Di Crescenzo, A., Giorno, V., Nobile, A.G.: An outline of theoretical and algorithmic approaches to first passage time problems with applications to biological modeling. Math. Japonica 50, 247–322 (1999)zbMATHGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2007

Authors and Affiliations

  • A. G. Nobile
    • 1
  • E. Pirozzi
    • 2
  • L. M. Ricciardi
    • 2
  1. 1.Dipartimento di Matematica e Informatica, Università di Salerno, Via Ponte don Melillo, Fisciano (SA)Italy
  2. 2.Dipartimento di Matematica e Applicazioni, Università di Napoli Federico II, Via Cintia, NapoliItaly

Personalised recommendations