TY - JOUR

T1 - Fractional diffusion equation for a power-law-truncated Lévy process

AU - Sokolov, I. M.

AU - Chechkin, A. V.

AU - Klafter, J.

N1 - Funding Information:
The authors thank professor M.H. Cohen for his fruitful discussions. IMS acknowledges partial financial support by the Fonds der Chemichen Industrie. AVC and JK acknowledge the support within the INTAS project.

PY - 2004/5/15

Y1 - 2004/5/15

N2 - Truncated Lévy flights are stochastic processes which display a crossover from a heavy-tailed Lévy behavior to a faster decaying probability distribution function (pdf). Putting less weight on long flights overcomes the divergence of the Lévy distribution second moment. We introduce a fractional generalization of the diffusion equation, whose solution defines a process in which a Lévy flight of exponent α is truncated by a power-law of exponent 5-α. A closed form for the characteristic function of the process is derived. The pdf of the displacement slowly converges to a Gaussian in its central part showing however a power-law far tail. Possible applications are discussed.

AB - Truncated Lévy flights are stochastic processes which display a crossover from a heavy-tailed Lévy behavior to a faster decaying probability distribution function (pdf). Putting less weight on long flights overcomes the divergence of the Lévy distribution second moment. We introduce a fractional generalization of the diffusion equation, whose solution defines a process in which a Lévy flight of exponent α is truncated by a power-law of exponent 5-α. A closed form for the characteristic function of the process is derived. The pdf of the displacement slowly converges to a Gaussian in its central part showing however a power-law far tail. Possible applications are discussed.

KW - Distributed-order diffusion equation

KW - Fractional kinetics

KW - Truncated Lévy flights

UR - http://www.scopus.com/inward/record.url?scp=1642617462&partnerID=8YFLogxK

U2 - 10.1016/j.physa.2003.12.044

DO - 10.1016/j.physa.2003.12.044

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AN - SCOPUS:1642617462

SN - 0378-4371

VL - 336

SP - 245

EP - 251

JO - Physica A: Statistical Mechanics and its Applications

JF - Physica A: Statistical Mechanics and its Applications

IS - 3-4

ER -