메뉴 건너뛰기




Volumn 152, Issue 4, 2013, Pages 742-752

Fokker-Planck Type Equations Associated with Subordinated Processes Controlled by Tempered α-stable Processes

Author keywords

Anomalous diffusion; Fokker Planck equation; Subordinated processes; Tempered stable processes

Indexed keywords


EID: 84881023852     PISSN: 00224715     EISSN: None     Source Type: Journal    
DOI: 10.1007/s10955-013-0754-4     Document Type: Article
Times cited : (5)

References (32)
  • 1
    • 0000078998 scopus 로고    scopus 로고
    • From continuous time random walks to the fractional Fokker-Planck equation
    • Barkai, E., Metzler, R., Klafter, J.: From continuous time random walks to the fractional Fokker-Planck equation. Phys. Rev. E 61, 132-138 (2000).
    • (2000) Phys. Rev. E , vol.61 , pp. 132-138
    • Barkai, E.1    Metzler, R.2    Klafter, J.3
  • 2
    • 84868254061 scopus 로고    scopus 로고
    • Strange kinetics of single molecules in living cells
    • Barkai, E., Garini, Y., Metzler, R.: Strange kinetics of single molecules in living cells. Phys. Today 65(8), 29 (2012).
    • (2012) Phys. Today , vol.65 , Issue.8 , pp. 29
    • Barkai, E.1    Garini, Y.2    Metzler, R.3
  • 3
    • 34047148984 scopus 로고    scopus 로고
    • Operators associated with a stochastic differential equation driven by fractional Brownian motions
    • Baudoin, F., Coutin, L.: Operators associated with a stochastic differential equation driven by fractional Brownian motions. Stoch. Process. Appl. 117, 550-574 (2007).
    • (2007) Stoch. Process. Appl. , vol.117 , pp. 550-574
    • Baudoin, F.1    Coutin, L.2
  • 5
    • 35248828149 scopus 로고    scopus 로고
    • On the fluid limit of the continuous-time random walk with general Lévy jump distribution functions
    • 041105
    • Cartea, Á., del-Castillo-Negrete, D.: On the fluid limit of the continuous-time random walk with general Lévy jump distribution functions. Phys. Rev. E 76, 041105 (2007).
    • (2007) Phys. Rev. E , vol.76
    • Cartea, Á.1    del-Castillo-Negrete, D.2
  • 7
    • 77954825229 scopus 로고    scopus 로고
    • Fractional Fokker-Planck equation with tempered α-stable waiting times: Langevin picture and computer simulation
    • 011117
    • Gajda, J., Magdziarz, M.: Fractional Fokker-Planck equation with tempered α-stable waiting times: Langevin picture and computer simulation. Phys. Rev. E 82, 011117 (2010).
    • (2010) Phys. Rev. E , vol.82
    • Gajda, J.1    Magdziarz, M.2
  • 8
    • 84864614781 scopus 로고    scopus 로고
    • On a timed-changed geometric Brownian motion and its application in financial market
    • Gu, H., Liang, J.-R., Zhang, Y.-X.: On a timed-changed geometric Brownian motion and its application in financial market. Acta Phys. Pol. B 43, 1667-1681 (2012).
    • (2012) Acta Phys. Pol. B , vol.43 , pp. 1667-1681
    • Gu, H.1    Liang, J.-R.2    Zhang, Y.-X.3
  • 9
    • 78651327329 scopus 로고    scopus 로고
    • Fokker-Planck-Kolmogorov equations associated with time-changed fractional Brownian motion
    • Hahn, M. G., Kobayashi, K., Umarov, S.: Fokker-Planck-Kolmogorov equations associated with time-changed fractional Brownian motion. Proc. Am. Math. Soc. 139, 691-705 (2011).
    • (2011) Proc. Am. Math. Soc. , vol.139 , pp. 691-705
    • Hahn, M.G.1    Kobayashi, K.2    Umarov, S.3
  • 10
    • 79952830793 scopus 로고    scopus 로고
    • On time-changed Gaussian processes and their associated Fokker-Planck-Kolmogorov equations
    • Hahn, M. G., Kobayashi, K., Ryvkina, J., Umarov, S.: On time-changed Gaussian processes and their associated Fokker-Planck-Kolmogorov equations. Electron. Commun. Probab. 16, 150-164 (2011).
    • (2011) Electron. Commun. Probab. , vol.16 , pp. 150-164
    • Hahn, M.G.1    Kobayashi, K.2    Ryvkina, J.3    Umarov, S.4
  • 12
    • 84868334608 scopus 로고    scopus 로고
    • Anomalous diffusion of phospholipids and cholesterols in a lipid bilayer and its origins
    • 188103
    • Jeon, J.-H., Monne, H. M.-S., Javanainen, M., Metzler, R.: Anomalous diffusion of phospholipids and cholesterols in a lipid bilayer and its origins. Phys. Rev. Lett. 109, 188103 (2012).
    • (2012) Phys. Rev. Lett. , vol.109
    • Jeon, J.-H.1    Monne, H.M.-S.2    Javanainen, M.3    Metzler, R.4
  • 13
    • 0001187166 scopus 로고
    • Wienersche Spiralen und einige andere interessante Kurven im Hilbertschen Raum
    • Kolmogorov, A. N.: Wienersche Spiralen und einige andere interessante Kurven im Hilbertschen Raum. C. R. (Dokl.) Acad. Sci. URSS (N. S.) 26, 115-118 (1940).
    • (1940) C. R. (Dokl.) Acad. Sci. URSS (N.S.) , vol.26 , pp. 115-118
    • Kolmogorov, A.N.1
  • 14
    • 54949102951 scopus 로고    scopus 로고
    • Stochastic modeling in nanoscale biophysics: subdiffusion within proteins
    • Kou, S. C.: Stochastic modeling in nanoscale biophysics: subdiffusion within proteins. Ann. Appl. Stat. 2, 501-535 (2008).
    • (2008) Ann. Appl. Stat. , vol.2 , pp. 501-535
    • Kou, S.C.1
  • 15
    • 19744382497 scopus 로고    scopus 로고
    • Generalized Langevin equation with fractional Gaussian noise: subdiffusion within a single protein molecule
    • 180603
    • Kou, S. C., Xie, X. S.: Generalized Langevin equation with fractional Gaussian noise: subdiffusion within a single protein molecule. Phys. Rev. Lett. 93, 180603 (2004).
    • (2004) Phys. Rev. Lett. , vol.93
    • Kou, S.C.1    Xie, X.S.2
  • 16
    • 84155189661 scopus 로고    scopus 로고
    • Fractional Fokker-Planck equation and Black-Scholes formula in composite-diffusive regime
    • Liang, J.-R., Wang, J., Lv, L.-J., Gu, H., Qiu, W.-Y., Ren, F.-Y.: Fractional Fokker-Planck equation and Black-Scholes formula in composite-diffusive regime. J. Stat. Phys. 146, 205-216 (2012).
    • (2012) J. Stat. Phys. , vol.146 , pp. 205-216
    • Liang, J.-R.1    Wang, J.2    Lv, L.-J.3    Gu, H.4    Qiu, W.-Y.5    Ren, F.-Y.6
  • 17
    • 69749117030 scopus 로고    scopus 로고
    • Stochastic representation of subdiffusion processes with time-dependent drift
    • Magdziarz, M.: Stochastic representation of subdiffusion processes with time-dependent drift. Stoch. Process. Appl. 119, 3238-3252 (2009).
    • (2009) Stoch. Process. Appl. , vol.119 , pp. 3238-3252
    • Magdziarz, M.1
  • 18
    • 84861498544 scopus 로고    scopus 로고
    • Anomalous dynamics of Black-Scholes model time-changed by inverse subordinators
    • Magdziarz, M., Gajda, J.: Anomalous dynamics of Black-Scholes model time-changed by inverse subordinators. Acta Phys. Pol. B 43, 1093-1110 (2012).
    • (2012) Acta Phys. Pol. B , vol.43 , pp. 1093-1110
    • Magdziarz, M.1    Gajda, J.2
  • 19
    • 33846621507 scopus 로고    scopus 로고
    • Fractional Fokker-Planck dynamics: stochastic representation and computer simulation
    • 016708
    • Magdziarz, M., Weron, A., Weron, K.: Fractional Fokker-Planck dynamics: stochastic representation and computer simulation. Phys. Rev. E 75, 016708 (2007).
    • (2007) Phys. Rev. E , vol.75
    • Magdziarz, M.1    Weron, A.2    Weron, K.3
  • 20
    • 56849094437 scopus 로고    scopus 로고
    • Equivalence of the fractional Fokker-Planck and subordinated Langevin equations: the case of a time-dependent force
    • 210601
    • Magdziarz, M., Weron, A., Klafter, J.: Equivalence of the fractional Fokker-Planck and subordinated Langevin equations: the case of a time-dependent force. Phys. Rev. Lett. 101, 210601 (2008).
    • (2008) Phys. Rev. Lett. , vol.101
    • Magdziarz, M.1    Weron, A.2    Klafter, J.3
  • 21
    • 0001407424 scopus 로고    scopus 로고
    • The fundamental solution of the space-time fractional diffusion equation
    • Mainardi, F., Luchko, Y., Pagnini, G.: The fundamental solution of the space-time fractional diffusion equation. Fract. Calc. Appl. Anal. 4(2), 153-192 (2001).
    • (2001) Fract. Calc. Appl. Anal. , vol.4 , Issue.2 , pp. 153-192
    • Mainardi, F.1    Luchko, Y.2    Pagnini, G.3
  • 22
    • 0000501589 scopus 로고
    • Fractional Brownian motions, fractional noises and applications
    • Mandelbrot, B. B., van Ness, J. W.: Fractional Brownian motions, fractional noises and applications. SIAM Rev. 10, 422-437 (1968).
    • (1968) SIAM Rev. , vol.10 , pp. 422-437
    • Mandelbrot, B.B.1    van Ness, J.W.2
  • 23
    • 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. 339, 1-77 (2000).
    • (2000) Phys. Rep. , vol.339 , pp. 1-77
    • Metzler, R.1    Klafter, J.2
  • 24
    • 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, Math. Gen. 37, R161-R208 (2004).
    • (2004) J. Phys. A, Math. Gen. , vol.37
    • Metzler, R.1    Klafter, J.2
  • 26
    • 13444309297 scopus 로고    scopus 로고
    • Models of anomalous diffusion: the subdiffusive case
    • Piryatinska, A., Saichev, A. I., Woyczynski, W. A.: Models of anomalous diffusion: the subdiffusive case. Physica A 349, 375-420 (2005).
    • (2005) Physica A , vol.349 , pp. 375-420
    • Piryatinska, A.1    Saichev, A.I.2    Woyczynski, W.A.3
  • 27
    • 34247641640 scopus 로고    scopus 로고
    • Tempering stable processes
    • Rosiński, J.: Tempering stable processes. Stoch. Process. Appl. 117, 677-707 (2007).
    • (2007) Stoch. Process. Appl. , vol.117 , pp. 677-707
    • Rosiński, J.1
  • 30
    • 56649084847 scopus 로고    scopus 로고
    • Diffusion and relaxation controlled by tempered α-stable processes
    • 051106
    • Stanislavsky, A., Weron, K., Weron, A.: Diffusion and relaxation controlled by tempered α-stable processes. Phys. Rev. E 78, 051106 (2008).
    • (2008) Phys. Rev. E , vol.78
    • Stanislavsky, A.1    Weron, K.2    Weron, A.3
  • 31
    • 41349119353 scopus 로고    scopus 로고
    • Complete description of all self-similar models driven by Lévy stable noise
    • 016113
    • Weron, A., Burnecki, K., Mercik, S., Weron, K.: Complete description of all self-similar models driven by Lévy stable noise. Phys. Rev. E 71, 016113 (2005).
    • (2005) Phys. Rev. E , vol.71
    • Weron, A.1    Burnecki, K.2    Mercik, S.3    Weron, K.4
  • 32
    • 84864426800 scopus 로고    scopus 로고
    • Arithmetic Brownian motion subordinated by tempered stable and inverse tempered stable processes
    • Wyłomańska, A.: Arithmetic Brownian motion subordinated by tempered stable and inverse tempered stable processes. Physica A 391, 5685-5696 (2012).
    • (2012) Physica A , vol.391 , pp. 5685-5696
    • Wyłomańska, A.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.