226
Views
29
CrossRef citations to date
0
Altmetric
Original Articles

An improved technique for the simulation of first passage times for diffusion processes

&
Pages 1135-1163 | Received 01 Jan 1998, Published online: 27 Jun 2007

References

  • Arnold , L. , Arnold , L. , Arnold , L. and Arnold , L. 1974 . Stochastic Differential Equations: Theory and Applications , Wiley .
  • Baldi , P. 1995 . “Exact asymptotics for the probability of exit from a domain and applications to simulations” . The Annals of Probability , 23 : 1644 – 1670 .
  • Ball , C.A. and Roma , A. 1993 . “A jump diffusion model for European monetary system” . Journal of International Money and Finance , 12 : 475 – 492 .
  • Buonocore , A. , Nobile , A.G. and Ricciardi , L.M. 1987 . “A new integral equation for the evaluation of first-passage-time probability densities” . Adv. Appl. Prob , 19 : 784 – 800 .
  • Cox , J.R. and Miller , H.D. 1965 . The theory of stochastic processes , Wiley .
  • Cerbone , G. , Ricciardi , L.M. and Sacerdote , L. 1981 . “Mean, variance and skewness of the first passage time for the Ornstein-Uhlenbeck process” . Cybern. Syst , 12 : 395 – 429 .
  • Di Crescenzo , A. and Nobile , A.G. 1995 . “Diffusion approximation to a queueing system with time-dependent arrival and service rates” . Queueing Systems , 19 : 41 – 62 .
  • Favella , L. , Reineri , M.T. , Ricciardi , L.M. and Sacerdote , L. 1982 . “First passage times problems and some related computational methods” . Cybern. Syst , 13 : 95 – 128 .
  • Fortet , R. 1943 . “Les functiones aléatoires du type de Markov associées à certaines équationes linéaires aux dérivées partielles du type parabolique” . J. Math. Pures Appl , 22 : 177 – 243 .
  • Giorno , V. , Nobile , A.G. and Ricciardi , L.M. 1986 . “On some diffusion approximations to queueing systems” . Adv. Appl. Prob , 18 : 991 – 1014 .
  • Giorno , V. , Lánský , P. , Nobile , A.G. and Ricciardi , L.M. 1988 . “Diffusion approximation and first-passage-time problem for a model neuron. III. A birth-and-death approach” . Biol. Cybern , 58 : 387 – 404 .
  • Giorno , V. , Nobile , A.G. , Ricciardi , L.M. and Sato , S. 1989 . “On the evaluation of first-passage-time probability densities via non-singular integral equations” . Adv. Appl. Prob , 21 : 20 – 36 .
  • Heath , R.A. 1981 . “A tandem random walk model for psychological discrimination” . Br. J. Math. Statist. Psychol , 34 : 76 – 92 .
  • Honerkamp, J. (1994). Stochastic Dynamical Systems: Concepts, Numerical Methods, Data Analysis, VCH.
  • Karlin , S. and Taylor , H.M. 1981 . A Second Course in Stochastic Processes , Academic Press .
  • Kloeden , P.E. and Platen , E. 1992 . The Numerical Solution of Stochastic Differential Equations , Springer Verlag .
  • Lánský , P. and Lánská , V. 1994 . “First-Passage-Time problem for simulated stochastic diffusion processes” . Comput. Biol. Med , 24 : 91 – 101 .
  • Maruyama , T. 1977 . “ Lectures Notes in Biomathematics ” . In Stochastic Problems in Population Genetics , Vol. 17 , Springer Verlag .
  • Ozaki , T. , Jimenez , J.C. and Haggan-Ozaki , V. 1996 . “The Role of the Likelihood Function in the Estimation of Chaos Models” . Manchester Center for Statistical Science, UMEST Department of Mathematics , 17 Technical Report 11/96
  • Platen , E. and Wagner , W. 1983 . On a Taylor formula for a class of ltô processes . Prob. Math. Statist , 3 ( 1 ) : 37 – 51 .
  • Ratcliff , R. 1980 . “A note on modelling accumulation of information when the rate of accumulation changes with time” . J. Math. Psycho , 21 ( 1 ) : 178 – 184 .
  • Ricciardi , L.M. 1977 . “ Lectures Notes in Biomathematics, n. 14 ” . In Diffusion Processes and Related Topics in Biology , Springer Verlag .
  • Ricciardi , L.M. and Sacerdote , L. 1979 . “The Ornstein-Uhlenbeck process as a model for neuronal activity” . Biol. Cybern , 35 : 1 – 9 .
  • Ricciardi , L.M. , Sacerdote , L. and Sato , S. 1984 . “On an integral equation for first-passage-tim e probability densities” . J. Appl. Prob , 21 : 302 – 314 .
  • Ricciardi , L.M. and Sato , S. 1990 . “Diffusion processes and first-passage -time problems” . In Lectures in Applied Mathematics and Informatics , Edited by: Ricciardi , L.M. Manchester University Press .
  • Sacerdote , L. and Tomassetti , F. 1996 . “On evaluations and asymptotic approximations of first-passage-time probabilities” . Adv. Appl. Prob , 28 : 270 – 284 .
  • Strittmatter , W. 1987 . “Numerical simulation of the mean first passage time” . University Freiburg . THEP 87/12

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.