메뉴 건너뛰기




Volumn 15, Issue , 2010, Pages 684-709

Poisson-type processes governed by fractional and higher-order recursive differential equations

Author keywords

Cox process; Fractional difference differential equations; Fractional Poisson processes; Generalized Mittag Leffler functions; Processes with random time; Renewal function

Indexed keywords


EID: 77953157380     PISSN: None     EISSN: 10836489     Source Type: Journal    
DOI: 10.1214/EJP.v15-762     Document Type: Article
Times cited : (103)

References (30)
  • 1
    • 41849099197 scopus 로고    scopus 로고
    • Pseudoprocesses governed by higher-order fractional differential equations
    • 60048
    • Beghin, L. (2008), Pseudoprocesses governed by higher-order fractional differential equations, Electronic Journ. Prob., 13, n.16, 467-485. (2009g:60048)
    • (2008) Electronic Journ. Prob. , vol.13 , Issue.16 , pp. 467-485
    • Beghin, L.1
  • 2
    • 70349472846 scopus 로고    scopus 로고
    • Fractional Poisson processes and related planar random motions
    • Beghin, L., Orsingher, E. (2009), Fractional Poisson processes and related planar random motions, Electronic Journ. Prob., 14, n.61, 1790-1826.
    • (2009) Electronic Journ. Prob. , vol.14 , Issue.61 , pp. 1790-1826
    • Beghin, L.1    Orsingher, E.2
  • 6
    • 0035439048 scopus 로고    scopus 로고
    • On random motions with velocities alternating at Erlang-distributed random times
    • MR1860096 (, h:60231)
    • Di Crescenzo, A. (2001), On random motions with velocities alternating at Erlang-distributed random times, Adv. inAppl. Probab. 33 (3), 690-701.MR1860096 (2002h:60231)
    • (2001) Adv. Inappl. Probab , vol.33 , Issue.3 , pp. 690-701
    • Di Crescenzo, A.1
  • 7
    • 0345099594 scopus 로고    scopus 로고
    • Exact transient analysis of a planar random motion with three directions
    • (, :60091)
    • Di Crescenzo, A. (2002), Exact transient analysis of a planar random motion with three directions, Stoch. Stoch. Rep., 72, n. 3-4, 175-189. (2003c:60091)
    • (2002) Stoch. Stoch. Rep. , vol.72 , Issue.3-4 , pp. 175-189
    • Di Crescenzo, A.1
  • 8
    • 0002847893 scopus 로고    scopus 로고
    • Fractional calculus, integral and differential equations of fractional order
    • Springer Verlag, Wien, n., Series CISM Courses and Lecture Notes, . (99g:26015)
    • Gorenflo R., Mainardi F. (1997), Fractional calculus, integral and differential equations of fractional order, in Fractals and Fractional Calculus in Continuum Mechanics, A.Carpinteri and F.Mainardi Editors, Springer Verlag, Wien, n.378, Series CISM Courses and Lecture Notes, 223-276. (99g:26015)
    • (1997) Fractals and Fractional Calculus in Continuum Mechanics, A.Carpinteri and F.Mainardi Editors , Issue.378 , pp. 223-276
    • Gorenflo, R.1    Mainardi, F.2
  • 9
    • 0003498504 scopus 로고    scopus 로고
    • Translated from the Russian. Sixth edition. Translation edited and with a preface by Alan Jeffrey and Daniel Zwillinger. Academic Press, Inc., San Diego, CA, (2001c:00002)
    • Gradshteyn, I. S., Ryzhik, I. M. (2000), Table of integrals, series, and products. Translated from the Russian. Sixth edition. Translation edited and with a preface by Alan Jeffrey and Daniel Zwillinger. Academic Press, Inc., San Diego, CA. (2001c:00002)
    • (2000) Table of Integrals, Series, and Products.
    • Gradshteyn, I.S.1    Ryzhik, I.M.2
  • 10
    • 0035480489 scopus 로고    scopus 로고
    • Fractional master equation: Non-standard analysis and Liouville-Riemann derivative
    • (2003i:82069)
    • Jumarie, G. (2001), Fractional master equation: non-standard analysis and Liouville-Riemann derivative, Chaos, Solitons and Fractals, 12, 2577-2587. (2003i:82069)
    • (2001) Chaos, Solitons and Fractals , vol.12 , pp. 2577-2587
    • Jumarie, G.1
  • 11
    • 33846070709 scopus 로고    scopus 로고
    • Cyclic random motions in Rd-space with n direction
    • (2007k:60036)
    • Lachal, A. (2006), Cyclic random motions in Rd-space with n direction,. ESAIMProbab. Stat,. 10, 277-316. (2007k:60036)
    • (2006) Esaimprobab. Stat , vol.10 , pp. 277-316
    • Lachal, A.1
  • 12
    • 33645337381 scopus 로고    scopus 로고
    • A renewal-process-type expression for the moments of inverse subor-dinators
    • (2007c:60089)
    • Lageras, A. N (2005), A renewal-process-type expression for the moments of inverse subor-dinators, Journ. Of Applied Prob., 42, 1134-1144. (2007c:60089)
    • (2005) Journ. Of Applied Prob. , vol.42 , pp. 1134-1144
    • Lageras, A.N.1
  • 14
    • 30244460855 scopus 로고    scopus 로고
    • The fundamental solutions for the fractional diffusion-wave equation
    • (97h:35132)
    • Mainardi F. (1996), The fundamental solutions for the fractional diffusion-wave equation, Applied Mathematics Letters, 9, n.6, 23-28. (97h:35132)
    • (1996) Applied Mathematics Letters , vol.9 , Issue.6 , pp. 23-28
    • Mainardi, F.1
  • 15
    • 0030464353 scopus 로고    scopus 로고
    • Fractional relaxation-oscillation and fractional diffusion-wave phenomena
    • (97i:26011)
    • Mainardi F. (1996), Fractional relaxation-oscillation and fractional diffusion-wave phenomena, Chaos, Solitons and Fractals, 7, n.9, 1461-1477. (97i:26011)
    • (1996) Chaos, Solitons and Fractals , vol.7 , Issue.9 , pp. 1461-1477
    • Mainardi, F.1
  • 17
    • 32544461435 scopus 로고    scopus 로고
    • A fractional generalization of the Poisson processes
    • Mainardi F., Gorenflo R., Scalas E. (2004), A fractional generalization of the Poisson processes, Vietnam Journ. Math., 32, 53-64.
    • (2004) Vietnam Journ. Math. , vol.32 , pp. 53-64
    • Mainardi, F.1    Gorenflo, R.2    Scalas, E.3
  • 20
    • 0742323831 scopus 로고    scopus 로고
    • Time-fractional equations and telegraph processes with Brownian time
    • (2005a:60056)
    • Orsingher, E., Beghin, L. (2004), Time-fractional equations and telegraph processes with Brownian time, Probability Theory and Related Fields, 128, 141-160. (2005a:60056)
    • (2004) Probability Theory and Related Fields , vol.128 , pp. 141-160
    • Orsingher, E.1    Beghin, L.2
  • 21
    • 63049113652 scopus 로고    scopus 로고
    • Fractional diffusion equations and processes with randomly-varying time
    • (2010b:60116)
    • Orsingher, E., Beghin, L. (2009), Fractional diffusion equations and processes with randomly-varying time, Annals of Probability, 37 (1), 206-249. (2010b:60116)
    • (2009) Annals of Probability , vol.37 , Issue.1 , pp. 206-249
    • Orsingher, E.1    Beghin, L.2
  • 23
    • 70449520832 scopus 로고    scopus 로고
    • One-dimensional semi-Markov evolutions with general Erlang sojourn times
    • (2007g:60107)
    • Pogorui, A.A., Rodriguez-Dagnino, R.M. (2005), One-dimensional semi-Markov evolutions with general Erlang sojourn times, Random Oper. Stoch. Equat., 13, (4), 399-405. (2007g:60107)
    • (2005) Random Oper. Stoch. Equat , vol.13 , Issue.4 , pp. 399-405
    • Pogorui, A.A.1    Rodriguez-Dagnino, R.M.2
  • 24
    • 0842337110 scopus 로고
    • A singular integral equation with a generalized Mittag Leffler function in the kernel
    • Prabhakar T.R. (1971), A singular integral equation with a generalized Mittag Leffler function in the kernel, Yokohama Math. J. 19, 7-15.
    • (1971) Yokohama Math. J. , vol.19 , pp. 7-15
    • Prabhakar, T.R.1
  • 26
    • 77953173395 scopus 로고    scopus 로고
    • Single server queue with batch arrivals and a-Poisson distribution
    • (2007m:60282)
    • Saji Kumar YR., Pillai, R.N. (2006), Single server queue with batch arrivals and a-Poisson distribution, Calcutta Stat. Assoc. Bull., 58, n.229-230, 93-103. (2007m:60282)
    • (2006) Calcutta Stat. Assoc. Bull. , vol.58 , Issue.229-230 , pp. 93-103
    • Saji Kumar, Y.R.1    Pillai, R.N.2
  • 28
    • 65549118001 scopus 로고    scopus 로고
    • Solutions of fractional reaction-diffusion equations in terms of Mittag-Leffler functions
    • arXiv:0708.2265 (August 2007)
    • Saxena, R.K., Mathai, A.M., Haubold, H.J., (2006), Solutions of fractional reaction-diffusion equations in terms of Mittag-Leffler functions, Intern. Journ. Scient. Research, 15, 1-17. arXiv:0708.2265 (August 2007).
    • (2006) Intern. Journ. Scient. Research , vol.15 , pp. 1-17
    • Saxena, R.K.1    Mathai, A.M.2    Haubold, H.J.3
  • 29
    • 34548078160 scopus 로고    scopus 로고
    • On a generalization of Mittag-Leffler function and their properties
    • 33E12 (33C15 33E20 44A20)
    • Shukla A.K., Prajapati, J.C., (2007), On a generalization of Mittag-Leffler function and their properties, Journ. Math. Anal. Appl., 336, 797-811. 33E12 (33C15 33E20 44A20)
    • (2007) Journ. Math. Anal. Appl , vol.336 , pp. 797-811
    • Shukla, A.K.1    Prajapati, J.C.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.