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Volumn 403, Issue 2, 2013, Pages 532-546

Fractional Pearson diffusions

Author keywords

Eigenfunction expansion; Fractional derivative; Hitting time; Mittag Leffler function; Pearson diffusion; Stable process

Indexed keywords


EID: 84936847014     PISSN: 0022247X     EISSN: 10960813     Source Type: Journal    
DOI: 10.1016/j.jmaa.2013.02.046     Document Type: Article
Times cited : (115)

References (45)
  • 2
    • 70349349380 scopus 로고    scopus 로고
    • Series expansions for the first passage distribution of Wong-Pearson jump-diffusions
    • Avram F., Leonenko N.N., Rabehasaina L. Series expansions for the first passage distribution of Wong-Pearson jump-diffusions. Stoch. Anal. Appl. 2009, 27(4):770-796.
    • (2009) Stoch. Anal. Appl. , vol.27 , Issue.4 , pp. 770-796
    • Avram, F.1    Leonenko, N.N.2    Rabehasaina, L.3
  • 3
    • 79551695282 scopus 로고    scopus 로고
    • Parameter estimation for Fisher-Snedecor diffusion
    • Avram F., Leonenko N.N., Šuvak N. Parameter estimation for Fisher-Snedecor diffusion. Statistics 2011, 45(1):1-16.
    • (2011) Statistics , vol.45 , Issue.1 , pp. 1-16
    • Avram, F.1    Leonenko, N.N.2    Šuvak, N.3
  • 4
    • 0001311725 scopus 로고    scopus 로고
    • Stochastic solutions for fractional Cauchy problems
    • Baeumer B., Meerschaert M.M. Stochastic solutions for fractional Cauchy problems. Fract. Calc. Appl. Anal. 2001, 4:4811-5000.
    • (2001) Fract. Calc. Appl. Anal. , vol.4 , pp. 4811-5000
    • Baeumer, B.1    Meerschaert, M.M.2
  • 5
    • 63549089594 scopus 로고    scopus 로고
    • Brownian subordinators and fractional Cauchy problems
    • Baeumer B., Meerschaert M.M., Nane E. Brownian subordinators and fractional Cauchy problems. Trans. Amer. Math. Soc. 2009, 361:3915-3930.
    • (2009) Trans. Amer. Math. Soc. , vol.361 , pp. 3915-3930
    • Baeumer, B.1    Meerschaert, M.M.2    Nane, E.3
  • 6
    • 22244488845 scopus 로고    scopus 로고
    • Diffusion-type models with given marginal distribution and autocorrelation function
    • Bibby B.M., Skovgaard M.I., Sørensen M. Diffusion-type models with given marginal distribution and autocorrelation function. Bernoulli 2005, 11(2):191-220.
    • (2005) Bernoulli , vol.11 , Issue.2 , pp. 191-220
    • Bibby, B.M.1    Skovgaard, M.I.2    Sørensen, M.3
  • 7
    • 0009537077 scopus 로고
    • Limit theorems for occupation times of Markov processes
    • Bingham N.H. Limit theorems for occupation times of Markov processes. Z. Wahrscheinlichkeit. 1971, 17:1-22.
    • (1971) Z. Wahrscheinlichkeit. , vol.17 , pp. 1-22
    • Bingham, N.H.1
  • 8
    • 0030188159 scopus 로고    scopus 로고
    • Infinite divisibility of random variables and their integer parts
    • Bondesson L., Kristiansen G., Steutel F. Infinite divisibility of random variables and their integer parts. Statist. Probab. Lett. 1996, 28:271-278.
    • (1996) Statist. Probab. Lett. , vol.28 , pp. 271-278
    • Bondesson, L.1    Kristiansen, G.2    Steutel, F.3
  • 9
    • 84977255207 scopus 로고
    • Linear models of dissipation whose Q is almost frequency independent, Part II
    • Caputo M. Linear models of dissipation whose Q is almost frequency independent, Part II. Geophys. J. R. Astron. Soc. 1967, 13:529-539.
    • (1967) Geophys. J. R. Astron. Soc. , vol.13 , pp. 529-539
    • Caputo, M.1
  • 10
    • 70349315385 scopus 로고    scopus 로고
    • Parameter estimation for fractional transport: a particle tracking approach
    • Chakraborty P., Meerschaert M.M., Lim C.Y. Parameter estimation for fractional transport: a particle tracking approach. Water Resour. Res. 2009, 45:W10415.
    • (2009) Water Resour. Res. , vol.45 , pp. W10415
    • Chakraborty, P.1    Meerschaert, M.M.2    Lim, C.Y.3
  • 11
    • 0001205798 scopus 로고
    • A theory of the term structure of interest rates
    • Cox J.C., Ingersoll J.E., Ross S.A. A theory of the term structure of interest rates. Econometrica 1985, 53:385-407.
    • (1985) Econometrica , vol.53 , pp. 385-407
    • Cox, J.C.1    Ingersoll, J.E.2    Ross, S.A.3
  • 13
    • 84976701037 scopus 로고
    • On the theory of the Brownian movement
    • Einstein A. On the theory of the Brownian movement. Ann. Phys. 1906, 4(19):371-381.
    • (1906) Ann. Phys. , vol.4 , Issue.19 , pp. 371-381
    • Einstein, A.1
  • 14
    • 21344498327 scopus 로고
    • Generalized Jacobi weights, Christoffel functions, and Jacobi polynomials
    • Erdélyi T., Magnus A.P., Nevai P. Generalized Jacobi weights, Christoffel functions, and Jacobi polynomials. SIAM J. Math. Anal. 1994, 25:602-614.
    • (1994) SIAM J. Math. Anal. , vol.25 , pp. 602-614
    • Erdélyi, T.1    Magnus, A.P.2    Nevai, P.3
  • 15
    • 50249097592 scopus 로고    scopus 로고
    • The Pearson diffusions: a class of statistically tractable diffusion processes
    • Forman J.L., Sørensen M. The Pearson diffusions: a class of statistically tractable diffusion processes. Scand. J. Stat. 2008, 35:438-465.
    • (2008) Scand. J. Stat. , vol.35 , pp. 438-465
    • Forman, J.L.1    Sørensen, M.2
  • 17
    • 0141974618 scopus 로고    scopus 로고
    • Fractional diffusion processes: probability distribution and continuous time random walk
    • Gorenflo R., Mainardi F. Fractional diffusion processes: probability distribution and continuous time random walk. Lecture Notes in Phys. 2003, 621:148-166.
    • (2003) Lecture Notes in Phys. , vol.621 , pp. 148-166
    • Gorenflo, R.1    Mainardi, F.2
  • 19
    • 0007045475 scopus 로고
    • A Cauchy problem for evolution equations of fractional order
    • Kochubei A.N. A Cauchy problem for evolution equations of fractional order. Differential Equations 1989, 25:967-974.
    • (1989) Differential Equations , vol.25 , pp. 967-974
    • Kochubei, A.N.1
  • 20
    • 0000189685 scopus 로고
    • On analytical methods in probability theory
    • Über die analytischen Methoden in der Wahrscheinlichkeitsrechnung
    • Kolmogorov A.N. On analytical methods in probability theory. Math. Ann. 1931, 104:415-458.
    • (1931) Math. Ann. , vol.104 , pp. 415-458
    • Kolmogorov, A.N.1
  • 21
    • 18844468150 scopus 로고    scopus 로고
    • Two families of functions related to the fractional powers of generators of strongly continuous contraction semigroups
    • Krägeloh A.M. Two families of functions related to the fractional powers of generators of strongly continuous contraction semigroups. J. Math. Anal. Appl. 2003, 283:459-467.
    • (2003) J. Math. Anal. Appl. , vol.283 , pp. 459-467
    • Krägeloh, A.M.1
  • 22
    • 70349330966 scopus 로고    scopus 로고
    • Statistical inference for reciprocal gamma diffusion processes
    • Leonenko N.N., Šuvak N. Statistical inference for reciprocal gamma diffusion processes. J. Statist. Plann. Inference 2010, 140:30-51.
    • (2010) J. Statist. Plann. Inference , vol.140 , pp. 30-51
    • Leonenko, N.N.1    Šuvak, N.2
  • 23
    • 78049505702 scopus 로고    scopus 로고
    • Statistical inference for Student diffusion process
    • Leonenko N.N., Šuvak N. Statistical inference for Student diffusion process. Stoch. Anal. Appl. 2010, 28(6):972-1002.
    • (2010) Stoch. Anal. Appl. , vol.28 , Issue.6 , pp. 972-1002
    • Leonenko, N.N.1    Šuvak, N.2
  • 24
    • 70349309658 scopus 로고    scopus 로고
    • Black-Scholes formula in subdiffusive regime
    • Magdziarz M. Black-Scholes formula in subdiffusive regime. J. Stat. Phys. 2009, 136:553-564.
    • (2009) J. Stat. Phys. , vol.136 , pp. 553-564
    • Magdziarz, M.1
  • 25
    • 33846621507 scopus 로고    scopus 로고
    • Fractional Fokker-Planck dynamics: stochastic representation and computer simulation
    • Magdziarz M., Weron A., Weron K. Fractional Fokker-Planck dynamics: stochastic representation and computer simulation. Phys. Rev. E 2007, 75:016708.
    • (2007) Phys. Rev. E , vol.75 , pp. 016708
    • Magdziarz, M.1    Weron, A.2    Weron, K.3
  • 26
    • 0000145521 scopus 로고    scopus 로고
    • On Mittag-Leffler-type functions in fractional evolution processes
    • Mainardi F., Gorenflo R. On Mittag-Leffler-type functions in fractional evolution processes. J. Comput. Appl. Math. 2000, 118(1-2):283-299.
    • (2000) J. Comput. Appl. Math. , vol.118 , Issue.1-2 , pp. 283-299
    • Mainardi, F.1    Gorenflo, R.2
  • 27
    • 70449607356 scopus 로고    scopus 로고
    • Fractional Cauchy problems on bounded domains
    • Meerschaert M.M., Nane E., Vellaisamy P. Fractional Cauchy problems on bounded domains. Ann. Probab. 2009, 37(3):979-1007.
    • (2009) Ann. Probab. , vol.37 , Issue.3 , pp. 979-1007
    • Meerschaert, M.M.1    Nane, E.2    Vellaisamy, P.3
  • 28
    • 4043102385 scopus 로고    scopus 로고
    • Limit theorems for continuous time random walks with infinite mean waiting times
    • Meerschaert M.M., Scheffler H.-P. Limit theorems for continuous time random walks with infinite mean waiting times. J. Appl. Probab. 2004, 41:623-638.
    • (2004) J. Appl. Probab. , vol.41 , pp. 623-638
    • Meerschaert, M.M.1    Scheffler, H.-P.2
  • 30
    • 0002641421 scopus 로고    scopus 로고
    • The random walk's guide to anomalous diffusion: a fractional dynamics approach
    • Metzler R., Klafter J. The random walk's guide to anomalous diffusion: a fractional dynamics approach. Phys. Rep. 2000, 339:1-77.
    • (2000) Phys. Rep. , vol.339 , pp. 1-77
    • Metzler, R.1    Klafter, J.2
  • 31
    • 4043151477 scopus 로고    scopus 로고
    • The restaurant at the end of the random walk: recent developments in the description of anomalous transport by fractional dynamics
    • Metzler R., Klafter J. The restaurant at the end of the random walk: recent developments in the description of anomalous transport by fractional dynamics. J. Phys. A 2004, 37:R161-R208.
    • (2004) J. Phys. A , vol.37 , pp. R161-R208
    • Metzler, R.1    Klafter, J.2
  • 33
    • 84936849031 scopus 로고    scopus 로고
    • Pointwise Fourier inversion and related Jacobi polynomial expansions
    • Walter de Gruyter, V. Bergelson, P. March, J. Rosenblatt (Eds.)
    • Pinsky M.A. Pointwise Fourier inversion and related Jacobi polynomial expansions. Convergence in Ergodic Theory and Probability 1996, Walter de Gruyter. V. Bergelson, P. March, J. Rosenblatt (Eds.).
    • (1996) Convergence in Ergodic Theory and Probability
    • Pinsky, M.A.1
  • 37
    • 33747342539 scopus 로고    scopus 로고
    • Five years of continuous-time random walks in econophysics
    • Scalas E. Five years of continuous-time random walks in econophysics. Complex Netw. Econ. Interactions 2006, 567:3-16.
    • (2006) Complex Netw. Econ. Interactions , vol.567 , pp. 3-16
    • Scalas, E.1
  • 39
    • 77649096334 scopus 로고    scopus 로고
    • Dependency without copulas and ellipticity
    • Shaw W.T., Manir A. Dependency without copulas and ellipticity. Eur. J. Finance 2009, 15(7-8):661-674.
    • (2009) Eur. J. Finance , vol.15 , Issue.7-8 , pp. 661-674
    • Shaw, W.T.1    Manir, A.2
  • 40
    • 31144434675 scopus 로고    scopus 로고
    • From diffusion to anomalous diffusion: a century after Einstein's Brownian motion
    • Sokolov I.M., Klafter J. From diffusion to anomalous diffusion: a century after Einstein's Brownian motion. Chaos 2005, 15:026103.
    • (2005) Chaos , vol.15 , pp. 026103
    • Sokolov, I.M.1    Klafter, J.2
  • 41
    • 0037442596 scopus 로고    scopus 로고
    • Black-Scholes model under subordination
    • Stanislavsky A.A. Black-Scholes model under subordination. Physica A 2009, 318:469-474.
    • (2009) Physica A , vol.318 , pp. 469-474
    • Stanislavsky, A.A.1
  • 43
    • 36149005118 scopus 로고
    • On the theory of Brownian motion
    • Uhlenbeck G.E., Ornstein L.S. On the theory of Brownian motion. Phys. Rev. 1930, 36:823-841.
    • (1930) Phys. Rev. , vol.36 , pp. 823-841
    • Uhlenbeck, G.E.1    Ornstein, L.S.2
  • 45
    • 62349083202 scopus 로고    scopus 로고
    • Particle tracking for time-fractional diffusion
    • Zhang Y., Meerschaert M.M., Baeumer B. Particle tracking for time-fractional diffusion. Phys. Rev. E 2008, 78:036705.
    • (2008) Phys. Rev. E , vol.78 , pp. 036705
    • Zhang, Y.1    Meerschaert, M.M.2    Baeumer, B.3


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