메뉴 건너뛰기




Volumn 6, Issue 3, 2004, Pages 323-341

Almost sure comparisons for first passage times of diffusion processes through boundaries

Author keywords

Comparison theorem; Diffusion process; Feller process; First passage time; Ornstein Uhlenbeck process

Indexed keywords


EID: 25844435865     PISSN: 13875841     EISSN: 15737713     Source Type: Journal    
DOI: 10.1023/B:MCAP.0000026563.27820.ff     Document Type: Review
Times cited : (3)

References (35)
  • 2
  • 3
    • 21844485889 scopus 로고
    • Diffusion approximation to a queueing system with time-dependent arrival and service rates
    • A. Di Crescenzo and A. G. Nobile, "Diffusion approximation to a queueing system with time-dependent arrival and service rates," Queueing Systems vol. 19 pp. 41-62, 1995.
    • (1995) Queueing Systems , vol.19 , pp. 41-62
    • Di Crescenzo, A.1    Nobile, A.G.2
  • 5
    • 0030607391 scopus 로고    scopus 로고
    • Comparing flrst-passage-times for semi-Markov skip-free processes
    • A. Di Crescenzo and L. M. Ricciardi, "Comparing flrst-passage-times for semi-Markov skip-free processes," Star. Prob. Lett. vol. 30 pp. 247-256, 1996.
    • (1996) Star. Prob. Lett. , vol.30 , pp. 247-256
    • Di Crescenzo, A.1    Ricciardi, L.M.2
  • 6
    • 0035369896 scopus 로고    scopus 로고
    • On a discrimination problem for a class of stochastic processes with ordered first-passage times
    • A. Di Crescenzo and L. M. Ricciardi, "On a discrimination problem for a class of stochastic processes with ordered first-passage times," Appl. Stoch. Models Bus. Ind. vol. 17 pp. 205-219, 2001.
    • (2001) Appl. Stoch. Models Bus. Ind. , vol.17 , pp. 205-219
    • Di Crescenzo, A.1    Ricciardi, L.M.2
  • 7
    • 0019938965 scopus 로고
    • A note on a comparison theorem for equations with different diffusions
    • L. I. Gal'čuk and M. H. A. Davis, "A note on a comparison theorem for equations with different diffusions," Stochastics vol. 6 pp. 147-149, 1982.
    • (1982) Stochastics , vol.6 , pp. 147-149
    • Gal'čuk, L.I.1    Davis, M.H.A.2
  • 8
    • 0023939939 scopus 로고
    • Diffusion approximation and first-passage-time problem for a model neuron. III. A birth-and-death approach
    • V. Giorno, P. Lánský, A. G. Nobile, and L. M. Ricciardi, "Diffusion approximation and first-passage-time problem for a model neuron. III. A birth-and-death approach," Biol. Cybern, vol. 58 pp. 387-404, 1988.
    • (1988) Biol. Cybern , vol.58 , pp. 387-404
    • Giorno, V.1    Lánský, P.2    Nobile, A.G.3    Ricciardi, L.M.4
  • 9
    • 0000602740 scopus 로고
    • On the evaluation of first-passage-time probability densities via non-singular integral equations
    • V. Giorno, A. G. Nobile, L. M. Ricciardi, and S. Sato, "On the evaluation of first-passage-time probability densities via non-singular integral equations," Adv. Appl. Prob. vol. 21 pp. 20-36, 1989.
    • (1989) Adv. Appl. Prob. , vol.21 , pp. 20-36
    • Giorno, V.1    Nobile, A.G.2    Ricciardi, L.M.3    Sato, S.4
  • 10
    • 28244454609 scopus 로고    scopus 로고
    • An improved technique for thesimulation of first passage times for diffusion processes
    • M. T. Giraudo and L. Sacerdote, "An improved technique for thesimulation of first passage times for diffusion processes," Commun. Statist.-Simula. vol. 28 pp. 1135-1163, 1999.
    • (1999) Commun. Statist.-simula. , vol.28 , pp. 1135-1163
    • Giraudo, M.T.1    Sacerdote, L.2
  • 11
    • 0003260362 scopus 로고    scopus 로고
    • A MonteCarlo method for the simulation of first passage times of diffusion processes
    • M. T. Giraudo, L. Sacerdote, and C. Zucca, "A MonteCarlo method for the simulation of first passage times of diffusion processes," Meth. Comp. Appl. Prob. vol. 3 pp. 215-231, 2001
    • (2001) Meth. Comp. Appl. Prob. , vol.3 , pp. 215-231
    • Giraudo, M.T.1    Sacerdote, L.2    Zucca, C.3
  • 13
    • 84968518781 scopus 로고
    • A comparison theorem for solutions of stochastic differential equations and its applications
    • Z. Y. Huang, "A comparison theorem for solutions of stochastic differential equations and its applications," Proc. A.M.S. vol. 91 pp. 611-617, 1984.
    • (1984) Proc. A.M.S. , vol.91 , pp. 611-617
    • Huang, Z.Y.1
  • 14
    • 0040070950 scopus 로고
    • Stochastic differential equations and diffusion processes
    • N. Ikeda and S. Watanabe, "Stochastic differential equations and diffusion processes," North Holland Math. Lib. 1989.
    • (1989) North Holland Math. Lib.
    • Ikeda, N.1    Watanabe, S.2
  • 16
    • 0029394120 scopus 로고
    • On the comparison of Feller and Ornstein-Uhlenbeck models for neural activity
    • P. Lánský, L. Sacerdote, and F. Tomassetti, "On the comparison of Feller and Ornstein-Uhlenbeck models for neural activity," Biol. Cybern, vol. 73 pp. 457-465, 1995.
    • (1995) Biol. Cybern , vol.73 , pp. 457-465
    • Lánský, P.1    Sacerdote, L.2    Tomassetti, F.3
  • 17
    • 0031221750 scopus 로고    scopus 로고
    • Total positivity of Markov chains and the failure rate character of some first passage times
    • S. Lee and J. Lynch, "Total positivity of Markov chains and the failure rate character of some first passage times," Adv. Appl. Prob. vol. 29 pp. 713-732, 1997.
    • (1997) Adv. Appl. Prob. , vol.29 , pp. 713-732
    • Lee, S.1    Lynch, J.2
  • 18
    • 0000389404 scopus 로고
    • On the first passage times for Markov-processes with monotone convex transition kernels
    • H. J. Li and M. Shaked, "On the first passage times for Markov-processes with monotone convex transition kernels," Stoch. Proc. Appl. vol. 58 pp. 205-216, 1995.
    • (1995) Stoch. Proc. Appl. , vol.58 , pp. 205-216
    • Li, H.J.1    Shaked, M.2
  • 19
    • 0031082734 scopus 로고    scopus 로고
    • Ageing first-passage times of Markov processes: A matrix approach
    • H. J. Li and M. Shaked, "Ageing first-passage times of Markov processes: A matrix approach," J. Appl. Prob. vol. 34 pp. 1-13, 1997.
    • (1997) J. Appl. Prob. , vol.34 , pp. 1-13
    • Li, H.J.1    Shaked, M.2
  • 21
    • 0022116585 scopus 로고
    • Exponential trends of first-passage-time densities for a class of diffusion processes with steady-state distribution
    • A. G. Nobile, L. M. Ricciardi, and L. Sacerdote, "Exponential trends of first-passage-time densities for a class of diffusion processes with steady-state distribution," J. Appl. Prob. vol. 22 pp. 611-618, 1985.
    • (1985) J. Appl. Prob. , vol.22 , pp. 611-618
    • Nobile, A.G.1    Ricciardi, L.M.2    Sacerdote, L.3
  • 22
    • 0019145046 scopus 로고
    • A new comparison theorem for solutions of stochastic differential equations
    • G. L. O'Brien, "A new comparison theorem for solutions of stochastic differential equations," Stochastics vol. 3 pp. 245-249, 1980.
    • (1980) Stochastics , vol.3 , pp. 245-249
    • O'Brien, G.L.1
  • 23
    • 84861247422 scopus 로고
    • Comparison et non-confluence des solutions d'équations differentielles stochastiques unidimensionnelles
    • Y. Ouknine, "Comparison et non-confluence des solutions d'équations differentielles stochastiques unidimensionnelles," Probab. Math. Statist. vol. 11 pp. 37-46, 1990.
    • (1990) Probab. Math. Statist. , vol.11 , pp. 37-46
    • Ouknine, Y.1
  • 24
    • 0000530732 scopus 로고
    • Diffusion processes and related topics in biology
    • Springer Verlag: Berlin
    • L. M. Ricciardi, Diffusion Processes and Related Topics in Biology. Lecture Notes in Biomathematics vol. 14, Springer Verlag: Berlin, 1977.
    • (1977) Lecture Notes in Biomathematics , vol.14
    • Ricciardi, L.M.1
  • 25
    • 0018606356 scopus 로고
    • The Ornstein-Uhlenbeck process as a model for neuronal activity
    • L. M. Ricciardi and L. Sacerdote, "The Ornstein-Uhlenbeck process as a model for neuronal activity," Biol. Cybern, vol. 35 pp. 1-9, 1979.
    • (1979) Biol. Cybern , vol.35 , pp. 1-9
    • Ricciardi, L.M.1    Sacerdote, L.2
  • 26
    • 0003313083 scopus 로고
    • Diffusion processes and first-passage-time problems
    • L. M. Ricciardi, Ed. Manchester University Press: Manchester
    • L. M. Ricciardi and S. Sato, Diffusion processes and first-passage-time problems, Lectures in Applied Mathematics and Informatics, L. M. Ricciardi, Ed. Manchester University Press: Manchester, 1990
    • (1990) Lectures in Applied Mathematics and Informatics
    • Ricciardi, L.M.1    Sato, S.2
  • 27
    • 0034546809 scopus 로고    scopus 로고
    • A qualitative comparison of some diffusion models for neural activity via stochastic ordering
    • L. Sacerdote and C. E. Smith, "A qualitative comparison of some diffusion models for neural activity via stochastic ordering," Biol. Cybern, vol. 83 pp. 543-551, 2000.
    • (2000) Biol. Cybern , vol.83 , pp. 543-551
    • Sacerdote, L.1    Smith, C.E.2
  • 28
    • 0034504593 scopus 로고    scopus 로고
    • New parameter relationships determined via stochastic ordering for spike activity in a reversal potential neural model
    • L. Sacerdote and C. E. Smith, "New parameter relationships determined via stochastic ordering for spike activity in a reversal potential neural model," Biosystems vol. 58 pp. 59-65, 2000.
    • (2000) Biosystems , vol.58 , pp. 59-65
    • Sacerdote, L.1    Smith, C.E.2
  • 29
    • 0017810089 scopus 로고
    • On the moments of the firing interval of the diffusion approximated model neuron
    • S. Sato, "On the moments of the firing interval of the diffusion approximated model neuron," Math. Biosci. vol. 39 pp. 53-70, 1978.
    • (1978) Math. Biosci. , vol.39 , pp. 53-70
    • Sato, S.1
  • 30
    • 0001131987 scopus 로고
    • On the 1st passage times of pure jump-processes
    • M. Shaked and J. G. Shanthikumar, "On the 1st passage times of pure jump-processes," J. Appl. Prob. vol. 20 pp. 427-446, 1988.
    • (1988) J. Appl. Prob. , vol.20 , pp. 427-446
    • Shaked, M.1    Shanthikumar, J.G.2
  • 32
    • 0026584533 scopus 로고
    • A note on neuronal firing and input variability
    • C. E. Smith, "A note on neuronal firing and input variability," J. Theor. Biol. vol. 154 pp. 271-275, 1992.
    • (1992) J. Theor. Biol. , vol.154 , pp. 271-275
    • Smith, C.E.1
  • 34
    • 0012269578 scopus 로고
    • On a comparison theorem for solutions of stochastic differential equations and its applications
    • T. Yamada, "On a comparison theorem for solutions of stochastic differential equations and its applications," J. Math. Kyoto Univ. vol. 13-3 pp. 497-512, 1973.
    • (1973) J. Math. Kyoto Univ. , vol.13 , Issue.3 , pp. 497-512
    • Yamada, T.1
  • 35
    • 0002171410 scopus 로고
    • On the strong comparison theorems for solutions of stochastic differential equations
    • T. Yamada and Y. Ogura, "On the strong comparison theorems for solutions of stochastic differential equations," Z. Wahrsch. Verw. Gebiete vol. 56 pp. 3-19, 1981.
    • (1981) Z. Wahrsch. Verw. Gebiete , vol.56 , pp. 3-19
    • Yamada, T.1    Ogura, Y.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.