메뉴 건너뛰기




Volumn 64, Issue 10, 2012, Pages 3021-3036

Fractional governing equations for coupled random walks

Author keywords

Anomalous diffusion; Central limit theory; Continuous time random walk; Fractional calculus; Operator stable law

Indexed keywords

ANOMALOUS DIFFUSION; CENTRAL LIMIT THEORY; CONTINUOUS TIME RANDOM WALKS; FRACTIONAL CALCULUS; OPERATOR STABLE LAW;

EID: 84868210553     PISSN: 08981221     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.camwa.2011.10.010     Document Type: Article
Times cited : (53)

References (31)
  • 1
    • 0001479044 scopus 로고
    • Random walks with infinite spatial and temporal moments
    • M. Shlesinger, J. Klafter, and Y.M. Wong Random walks with infinite spatial and temporal moments J. Stat. Phys. 27 1982 499 512
    • (1982) J. Stat. Phys. , vol.27 , pp. 499-512
    • Shlesinger, M.1    Klafter, J.2    Wong, Y.M.3
  • 2
    • 0034032484 scopus 로고    scopus 로고
    • Application of a fractional advection-dispersion equation
    • DOI 10.1029/2000WR900031
    • D. Benson, S. Wheatcraft, and M. Meerschaert Application of a fractional advection-dispersion equation Water Resour. Res. 36 2000 1403 1412 (Pubitemid 30334241)
    • (2000) Water Resources Research , vol.36 , Issue.6 , pp. 1403-1412
    • Benson, D.A.1    Wheatcraft, S.W.2    Meerschaert, M.M.3
  • 4
    • 33845247896 scopus 로고    scopus 로고
    • Modeling non-Fickian transport in geological formations as a continuous time random walk
    • B. Berkowitz, A. Cortis, M. Dentz, and H. Scher Modeling non-Fickian transport in geological formations as a continuous time random walk Rev. Geophys. 44 2006 RG2003
    • (2006) Rev. Geophys. , vol.44 , pp. 2003
    • Berkowitz, B.1    Cortis, A.2    Dentz, M.3    Scher, H.4
  • 5
    • 77954316974 scopus 로고    scopus 로고
    • Fractional advection-dispersion equations for modeling transport at the Earth surface
    • R. Schumer, M.M. Meerschaert, and B. Baeumer Fractional advection-dispersion equations for modeling transport at the Earth surface J. Geophys. Res. 114 2009 F00A07
    • (2009) J. Geophys. Res. , vol.114
    • Schumer, R.1    Meerschaert, M.M.2    Baeumer, B.3
  • 6
    • 33947227320 scopus 로고    scopus 로고
    • Migration and proliferation dichotomy in tumor-cell invasion
    • S. Fedotov, and A. Iomin Migration and proliferation dichotomy in tumor-cell invasion Phys. Rev. Lett. 98 11 2007 8101
    • (2007) Phys. Rev. Lett. , vol.98 , Issue.11 , pp. 8101
    • Fedotov, S.1    Iomin, A.2
  • 7
    • 10044223573 scopus 로고    scopus 로고
    • Kinetics of protein-DNA interaction: Facilitated target location in sequence-dependent potential
    • DOI 10.1529/biophysj.104.050765
    • M. Slutsky, and L.A. Mirny Kinetics of protein-DNA interaction: facilitated target location in sequence-dependent potential Biophys. J. 87 2004 4021 4035 (Pubitemid 39602906)
    • (2004) Biophysical Journal , vol.87 , Issue.6 , pp. 4021-4035
    • Slutsky, M.1    Mirny, L.A.2
  • 9
    • 32544454809 scopus 로고    scopus 로고
    • Five years of continuous-time random walks in econophysics
    • A. Namatame (Ed.) Kyoto
    • E. Scalas, Five years of continuous-time random walks in econophysics, in: A. Namatame (Ed.), Proceedings of WEHIA 2004, Kyoto, 2004.
    • (2004) Proceedings of WEHIA 2004
    • Scalas, E.1
  • 10
    • 33644988392 scopus 로고    scopus 로고
    • Havriliak-Negami response in the framework of the continuous-time random walk
    • K. Weron, A. Jurlewicz, and M. Magdziarz Havriliak-Negami response in the framework of the continuous-time random walk Acta Phys. Polon. B 36 2005 1855 1868
    • (2005) Acta Phys. Polon. B , vol.36 , pp. 1855-1868
    • Weron, K.1    Jurlewicz, A.2    Magdziarz, M.3
  • 11
    • 77951526089 scopus 로고    scopus 로고
    • Overshooting and undershooting subordination scenario for fractional two-power-law relaxation responses
    • K. Weron, A. Jurlewicz, M. Magdziarz, A. Weron, and J. Trzmiel Overshooting and undershooting subordination scenario for fractional two-power-law relaxation responses Phys. Rev. E 81 2010 041123
    • (2010) Phys. Rev. e , vol.81 , pp. 041123
    • Weron, K.1    Jurlewicz, A.2    Magdziarz, M.3    Weron, A.4    Trzmiel, J.5
  • 12
    • 57349138205 scopus 로고    scopus 로고
    • Coupled continuous-time random walk approach to the Rachev- Rüschendorf model for financial data
    • A. Jurlewicz, A. Wyomaska, and P. ebrowski Coupled continuous-time random walk approach to the Rachev-Rüschendorf model for financial data Physica A 388 2009 407 418
    • (2009) Physica A , vol.388 , pp. 407-418
    • Jurlewicz, A.1    Wyomaska, A.2    Ebrowski, P.3
  • 15
    • 4043102385 scopus 로고    scopus 로고
    • Limit theorems for continuous-time random walks with infinite mean waiting times
    • DOI 10.1239/jap/1091543414
    • M.M. Meerschaert, and H.P. Scheffler Limit theorems for continuous time random walks with infinite mean waiting times J. Appl. Probab. 41 3 2004 623 638 (Pubitemid 39620503)
    • (2004) Journal of Applied Probability , vol.41 , Issue.3 , pp. 623-638
    • Meerschaert, M.M.1    Scheffler, H.-P.2
  • 16
    • 0004263072 scopus 로고
    • Lecture Notes in Mathematics Springer-Verlag Berlin
    • E. Seneta Regularly Varying Functions Lecture Notes in Mathematics vol. 508 1976 Springer-Verlag Berlin
    • (1976) Regularly Varying Functions , vol.508
    • Seneta, E.1
  • 18
    • 48349113290 scopus 로고    scopus 로고
    • Triangular array limits for continuous time random walks
    • M.M. Meerschaert, and H.P. Scheffler Triangular array limits for continuous time random walks Stoch. Proc. Appl. 118 2008 1606 1633
    • (2008) Stoch. Proc. Appl. , vol.118 , pp. 1606-1633
    • Meerschaert, M.M.1    Scheffler, H.P.2
  • 21
    • 78650298926 scopus 로고    scopus 로고
    • Lagging and leading coupled continuous time random walks, renewal times and their joint limits
    • P. Straka, and B.I. Henry Lagging and leading coupled continuous time random walks, renewal times and their joint limits Stoch. Proc. Appl. 121 2 2011 324 336
    • (2011) Stoch. Proc. Appl. , vol.121 , Issue.2 , pp. 324-336
    • Straka, P.1    Henry, B.I.2
  • 22
    • 26844520430 scopus 로고    scopus 로고
    • Limit theorems for mixed max-sum processes with renewal stopping
    • DOI 10.1214/105051604000000215
    • D.S. Silvestrov, and J.L. Teugels Limit theorems for mixed max-sum processes with renewal stopping Ann. Appl. Probab. 14 2004 1838 1868 (Pubitemid 41449197)
    • (2004) Annals of Applied Probability , vol.14 , Issue.4 , pp. 1838-1868
    • Silvestrov, D.S.1    Teugels, J.L.2
  • 24
  • 25
    • 0001637037 scopus 로고
    • Hitting probabilities of single points for processes with stationary independent increments
    • 129 p
    • H. Kesten Hitting probabilities of single points for processes with stationary independent increments Mem. Am. Math. Soc. 93 1969 129 p
    • (1969) Mem. Am. Math. Soc. , vol.93
    • Kesten, H.1
  • 26
    • 0001311725 scopus 로고    scopus 로고
    • Stochastic solutions for fractional Cauchy problems
    • B. Baeumer, and M.M. Meerschaert Stochastic solutions for fractional Cauchy problems Fract. Calc. Appl. Anal. 4 2001 481 500
    • (2001) Fract. Calc. Appl. Anal. , vol.4 , pp. 481-500
    • Baeumer, B.1    Meerschaert, M.M.2
  • 27
    • 0002641421 scopus 로고    scopus 로고
    • The random walk's guide to anomalous diffusion: A fractional dynamics approach
    • R. Metzler, and J. Klafter The random walk's guide to anomalous diffusion: a fractional dynamics approach Phys. Rep. 339 2000 1 77
    • (2000) Phys. Rep. , vol.339 , pp. 1-77
    • Metzler, R.1    Klafter, J.2
  • 28
    • 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
    • R. Metzler, and J. Klafter The restaurant at the end of the random walk: recent developments in the description of anomalous transport by fractional dynamics J. Phys. A 37 2004 R161 R208
    • (2004) J. Phys. A , vol.37
    • Metzler, R.1    Klafter, J.2
  • 29
    • 0035130739 scopus 로고    scopus 로고
    • Eulerian derivation of the fractional advection-dispersion equation
    • DOI 10.1016/S0169-7722(00)00170-4, PII S0169772200001704
    • R. Schumer, D.A. Benson, M.M. Meerschaert, and S.W. Wheatcraft Eulerian derivation of the fractional advection-dispersion equation J. Contam. Hydrol. 48 2001 69 88 (Pubitemid 32141059)
    • (2001) Journal of Contaminant Hydrology , vol.48 , Issue.1-2 , pp. 69-88
    • Schumer, R.1    Benson, D.A.2    Meerschaert, M.M.3    Wheatcraft, S.W.4
  • 30
    • 21844503941 scopus 로고
    • Asymptotic distributions of continuous-time random walks: A probabilistic approach
    • M. Kotulski Asymptotic distributions of the continuous time random walks: a probabilistic approach J. Stat. Phys. 81 1995 777 792 (Pubitemid 126000029)
    • (1995) Journal of Statistical Physics , vol.81 , Issue.3-4 , pp. 777-792
    • Kotulski, M.1
  • 31
    • 84868201892 scopus 로고
    • Translations of Mathematical Monographs American Mathematical Society Providence, RI Translated from the Russian by H.H. McFaden, Translation edited by Ben Silver
    • V.M. Zolotarev One-Dimensional Stable Distributions Translations of Mathematical Monographs vol. 65 1986 American Mathematical Society Providence, RI Translated from the Russian by H.H. McFaden, Translation edited by Ben Silver
    • (1986) One-Dimensional Stable Distributions , vol.65
    • Zolotarev, V.M.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.