@article{5d1d65d3928448929fcd4abd99fe5b6c,
title = "Fractional diffusion equation for a power-law-truncated L{\'e}vy process",
abstract = "Truncated L{\'e}vy flights are stochastic processes which display a crossover from a heavy-tailed L{\'e}vy behavior to a faster decaying probability distribution function (pdf). Putting less weight on long flights overcomes the divergence of the L{\'e}vy distribution second moment. We introduce a fractional generalization of the diffusion equation, whose solution defines a process in which a L{\'e}vy 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.",
keywords = "Distributed-order diffusion equation, Fractional kinetics, Truncated L{\'e}vy flights",
author = "Sokolov, {I. M.} and Chechkin, {A. V.} and J. Klafter",
note = "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.",
year = "2004",
month = may,
day = "15",
doi = "10.1016/j.physa.2003.12.044",
language = "אנגלית",
volume = "336",
pages = "245--251",
journal = "Physica A: Statistical Mechanics and its Applications",
issn = "0378-4371",
publisher = "Elsevier B.V.",
number = "3-4",
}