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Volumn 59, Issue 3, 1999, Pages 2736-2745

Lévy flights in external force fields: Langevin and fractional Fokker-Planck equations and their solutions

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EID: 0000687710     PISSN: 1063651X     EISSN: None     Source Type: Journal    
DOI: 10.1103/PhysRevE.59.2736     Document Type: Article
Times cited : (425)

References (63)
  • 41
    • 85037215509 scopus 로고    scopus 로고
    • P. Lévy, Calcul des Probabilités (Gauthier-Villars, Paris, 1925); Théorie de l’Addition des Variables Aléatoires (Gauthier-Villars, Paris, 1937)
    • P. Lévy, Calcul des Probabilités (Gauthier-Villars, Paris, 1925); Théorie de l’Addition des Variables Aléatoires (Gauthier-Villars, Paris, 1937).
  • 42
    • 0003513648 scopus 로고
    • Addison-Wesley, Reading, MA, W. Feller, An Introduction to Probability Theory and its Applications [Wiley, New York, 1957 (Vol. I) and 1966 (Vol. II)]
    • B. V. Gnedenko and A. N. Kolmogorov, Limit Distributions for Sums of Independent Random Variables (Addison-Wesley, Reading, MA, 1954);W. Feller, An Introduction to Probability Theory and its Applications [Wiley, New York, 1957 (Vol. I) and 1966 (Vol. II)].
    • (1954) Limit Distributions for Sums of Independent Random Variables
    • Gnedenko, B.V.1    Kolmogorov, A.N.2
  • 43
    • 85037222673 scopus 로고    scopus 로고
    • Lévy Flights and Related Topics in Physics, edited by M. F. Shlesinger, G. M. Zaslavsky, and U. Frisch, Lecture Notes in Physics Vol. 450 (Springer-Verlag, Berlin, 1994)
    • Lévy Flights and Related Topics in Physics, edited by M. F. Shlesinger, G. M. Zaslavsky, and U. Frisch, Lecture Notes in Physics Vol. 450 (Springer-Verlag, Berlin, 1994).
  • 44
    • 85037245009 scopus 로고    scopus 로고
    • A renormalization involving “(Formula presented)” and D has to be carried out in order to make the problem well defined 22
    • A renormalization involving “(Formula presented)” and D has to be carried out in order to make the problem well defined 22.
  • 45
    • 85037214085 scopus 로고    scopus 로고
    • This asymptotics could also be taken as the definition of the noise, with a cutoff (Formula presented) to account for normalizability 2122
    • This asymptotics could also be taken as the definition of the noise, with a cutoff (Formula presented) to account for normalizability 2122.
  • 51
    • 85037200414 scopus 로고    scopus 로고
    • A. M. Mathai and R. K. Saxena, The H-function with Applications in Statistics and Other Disciplines (Wiley Eastern, New Delhi, 1978)
    • A. M. Mathai and R. K. Saxena, The H-function with Applications in Statistics and Other Disciplines (Wiley Eastern, New Delhi, 1978).
  • 56
    • 85037250040 scopus 로고    scopus 로고
    • The scaling result (Formula presented) [Eq. (11)] and the squared absolute mean (Formula presented) [Eq. (12)] are proportional to (Formula presented) The divergence of the mean square displacement (Formula presented) can be avoided in the Lévy walk concept through the introduction of a time cost which penalizes long displacements. For Lévy walks, the proportionality (Formula presented) is found, see 18 40
    • The scaling result (Formula presented) [Eq. (11)] and the squared absolute mean (Formula presented) [Eq. (12)] are proportional to (Formula presented) The divergence of the mean square displacement (Formula presented) can be avoided in the Lévy walk concept through the introduction of a time cost which penalizes long displacements. For Lévy walks, the proportionality (Formula presented) is found, see 1840.


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.