Uncoupled continuous-time random walks: Solution and limiting behavior of the master equation

被引：159
作者：
Scalas, E
Gorenflo, R
Mainardi, F
机构：
[1] E Piedmont Univ, Dept Adv Sci & Technol, I-15100 Alessandria, Italy
[2] Free Univ Berlin, Inst Math 1, D-14195 Berlin, Germany
[3] Univ Bologna, Dept Phys, I-40126 Bologna, Italy
[4] Ist Nazl Fis Nucl, I-40126 Bologna, Italy
来源：
PHYSICAL REVIEW E | 2004年 / 69卷 / 01期
关键词：
D O I：
10.1103/PhysRevE.69.011107
中图分类号：
O35 [流体力学]; O53 [等离子体物理学];
学科分类号：
070204 ; 080103 ; 080704 ;
摘要：
A detailed study is presented for a large class of uncoupled continuous-time random walks. The master equation is solved for the Mittag-Leffler survival probability. The properly scaled diffusive limit of the master equation is taken and its relation with the fractional diffusion equation is discussed. Finally, some common objections found in the literature are thoroughly reviewed.
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页数：8
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共 66 条
[41]  
MASOLIVER J, CONDMAT0308017
[42]   Governing equations and solutions of anomalous random walk limits [J].
Meerschaert, MM ;
Benson, DA ;
Scheffler, HP ;
Becker-Kern, P .
PHYSICAL REVIEW E, 2002, 66 (06) :4-060102
[43]   Deriving fractional Fokker-Planck equations from a generalised master equation [J].
Metzler, R ;
Barkai, E ;
Klafter, J .
EUROPHYSICS LETTERS, 1999, 46 (04) :431-436
[44]   FRACTIONAL MODEL EQUATION FOR ANOMALOUS DIFFUSION [J].
METZLER, R ;
GLOCKLE, WG ;
NONNENMACHER, TF .
PHYSICA A, 1994, 211 (01) :13-24
[45]   The random walk's guide to anomalous diffusion: a fractional dynamics approach [J].
Metzler, R ;
Klafter, J .
PHYSICS REPORTS-REVIEW SECTION OF PHYSICS LETTERS, 2000, 339 (01) :1-77
[46]  
Montroll E. W., 1973, J STAT PHYS, V9, P101, DOI DOI 10.1007/BF01016843
[47]   RANDOM WALKS ON LATTICES .2. [J].
MONTROLL, EW ;
WEISS, GH .
JOURNAL OF MATHEMATICAL PHYSICS, 1965, 6 (02) :167-+
[48]  
Podlubny I., 1999, FRACTIONAL DIFFERENT
[49]   Waiting-times and returns in high-frequency financial data: an empirical study [J].
Raberto, M ;
Scalas, E ;
Mainardi, F .
PHYSICA A-STATISTICAL MECHANICS AND ITS APPLICATIONS, 2002, 314 (1-4) :749-755
[50]   CONTINUOUS-TIME RANDOM-WALKS AND THE FRACTIONAL DIFFUSION EQUATION [J].
ROMAN, HE ;
ALEMANY, PA .
JOURNAL OF PHYSICS A-MATHEMATICAL AND GENERAL, 1994, 27 (10) :3407-3410
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