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Volumn 28, Issue 1, 1996, Pages 270-284

On evaluations and asymptotic approximations of first-passage-time probabilities

Author keywords

Diffusion processes; Feller processes; First passage time; Orstein Uhlenbeck processes

Indexed keywords


EID: 0001737603     PISSN: 00018678     EISSN: None     Source Type: Journal    
DOI: 10.1017/S0001867800027361     Document Type: Review
Times cited : (28)

References (18)
  • 1
    • 0000307498 scopus 로고
    • Sur les opérations dans les ensembles abstraits et leur application aux équations intégrales
    • BANACH, S. (1922) Sur les opérations dans les ensembles abstraits et leur application aux équations intégrales. Fund. Mat. 3, 133-181.
    • (1922) Fund. Mat. , vol.3 , pp. 133-181
    • Banach, S.1
  • 2
    • 0001710327 scopus 로고
    • A new integral equation for the evaluation of the first-passage-time probability densities
    • BUONOCORE, A., NOBILE, A. G. AND RICCIARDI, L. M. (1987) A new integral equation for the evaluation of the first-passage-time probability densities. Adv. Appl. Prob. 19, 784-800.
    • (1987) Adv. Appl. Prob. , vol.19 , pp. 784-800
    • Buonocore, A.1    Nobile, A.G.2    Ricciardi, L.M.3
  • 3
    • 0001456827 scopus 로고
    • The minimum of stationary Markov process superimposed on a U-shaped trend
    • DANIELS, H. E. (1969) The minimum of stationary Markov process superimposed on a U-shaped trend. J. Appl. Prob. 6, 399-408.
    • (1969) J. Appl. Prob. , vol.6 , pp. 399-408
    • Daniels, H.E.1
  • 4
    • 0001199065 scopus 로고
    • The first passage problem for a continuous Markov process
    • DARLING, D. A. AND SIEGERT, A. J. F. (1953) The first passage problem for a continuous Markov process. Ann. Math. Statist. 24, 624-639.
    • (1953) Ann. Math. Statist. , vol.24 , pp. 624-639
    • Darling, D.A.1    Siegert, A.J.F.2
  • 5
    • 0001208970 scopus 로고
    • Boundary crossing probabilities for the Brownian motion and Poisson processes and techniques for computing the power of the Kolmogorov-Smirnov theorem
    • DURBIN, J. (1971) Boundary crossing probabilities for the Brownian motion and Poisson processes and techniques for computing the power of the Kolmogorov-Smirnov theorem. J. Appl. Prob. 8, 431-453.
    • (1971) J. Appl. Prob. , vol.8 , pp. 431-453
    • Durbin, J.1
  • 6
    • 0022023075 scopus 로고
    • The first-passage density of a Gaussian process to a general boundary
    • DURBIN, J. (1985) The first-passage density of a Gaussian process to a general boundary. J. Appl. Prob. 22, 99-122.
    • (1985) J. Appl. Prob. , vol.22 , pp. 99-122
    • Durbin, J.1
  • 7
    • 0001003734 scopus 로고
    • The first-passage density of the Brownian motion process to a curved boundary
    • DURBIN, J. (1992) The first-passage density of the Brownian motion process to a curved boundary. J. Appl. Prob. 29, 291-304.
    • (1992) J. Appl. Prob. , vol.29 , pp. 291-304
    • Durbin, J.1
  • 8
    • 0001556572 scopus 로고
    • Les fonctions aleatoires du type de Markoff associées à certaines equations linéaires aux derivées partielles du type parabolique
    • FORTET, R. (1943) Les fonctions aleatoires du type de Markoff associées à certaines equations linéaires aux derivées partielles du type parabolique. Math. Pures Appl. 21, 177-243.
    • (1943) Math. Pures Appl. , vol.21 , pp. 177-243
    • Fortet, R.1
  • 9
    • 0023939939 scopus 로고
    • Diffusion approximation and first-passage-time problem for a model neuron. III. A birth-and-death process approach
    • 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 process approach. Biol. Cybern. 58, 387-404.
    • (1988) Biol. Cybern. , vol.58 , pp. 387-404
    • Giorno, V.1    Lánský, P.2    Nobile, A.G.3    Ricciardi, L.M.4
  • 10
    • 0000602740 scopus 로고
    • On the evaluation of the first-passage-time probability densities via nonsingular integral equations
    • GIORNO, V., NOBILE, A. G., RICCIARDI, L. M. AND SATO, S. (1989) On the evaluation of the first-passage-time probability densities via nonsingular integral equations. Adv. Appl. Prob. 21, 20-36.
    • (1989) Adv. Appl. Prob. , vol.21 , pp. 20-36
    • Giorno, V.1    Nobile, A.G.2    Ricciardi, L.M.3    Sato, S.4
  • 13
    • 0022080254 scopus 로고
    • A note on first-passage-time and some related problems
    • NOBILE, A. G., RICCIARDI, L. M. AND SACERDOTE, L. (1985) A note on first-passage-time and some related problems. J. Appl. Prob. 22, 346-359.
    • (1985) J. Appl. Prob. , vol.22 , pp. 346-359
    • Nobile, A.G.1    Ricciardi, L.M.2    Sacerdote, L.3
  • 14
    • 0022082682 scopus 로고
    • Exponential trends of OrnsteinUhlenbeck first-passage-time densities
    • NOBILE, A. G., RICCIARDI, L. M. AND SACERDOTE, L. (1985) Exponential trends of OrnsteinUhlenbeck first-passage-time densities. J. Appl. Prob. 22, 360-369.
    • (1985) J. Appl. Prob. , vol.22 , pp. 360-369
    • Nobile, A.G.1    Ricciardi, L.M.2    Sacerdote, L.3
  • 15
    • 0022116585 scopus 로고
    • Exponential trends of first-passagetime densities for a class of diffusion processes with steady-state distribution
    • NOBILE, A. G., RICCIARDI, L. M. AND SACERDOTE, L. (1985) Exponential trends of first-passagetime densities for a class of diffusion processes with steady-state distribution. J. Appl. Prob. 22, 611-618.
    • (1985) J. Appl. Prob. , vol.22 , pp. 611-618
    • Nobile, A.G.1    Ricciardi, L.M.2    Sacerdote, L.3
  • 16
    • 0018606356 scopus 로고
    • The Ornstein-Uhlenbeck process as a model for neuronal activity. I. Mean and variance of the firing time
    • RICCIARDI, L. M. AND SACERDOTE, L. (1979) The Ornstein-Uhlenbeck process as a model for neuronal activity. I. Mean and variance of the firing time. Biol. Cybern. 35, 1-9.
    • (1979) Biol. Cybern. , vol.35 , pp. 1-9
    • Ricciardi, L.M.1    Sacerdote, L.2
  • 17
    • 0020750785 scopus 로고
    • Diffusion approximation and the first-passage-time problem for a model neuron. II Outline of computation method
    • RICCIARDI, L. M., SACERDOTE, L. AND SATO, S. (1983) Diffusion approximation and the first-passage-time problem for a model neuron. II Outline of computation method. Math. Biosci. 64, 29-44.
    • (1983) Math. Biosci. , vol.64 , pp. 29-44
    • Ricciardi, L.M.1    Sacerdote, L.2    Sato, S.3
  • 18
    • 0021451218 scopus 로고
    • On an integral equation for first-passagetime probability densities
    • RICCIARDI, L. M., SACERDOTE, L. AND SATO, S. (1984) On an integral equation for first-passagetime probability densities. J. Appl. Prob. 21, 302-314.
    • (1984) J. Appl. Prob. , vol.21 , pp. 302-314
    • Ricciardi, L.M.1    Sacerdote, L.2    Sato, S.3


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.