Stochastic representation of subdiffusion processes with time-dependent drift

STOCHASTIC PROCESSES AND THEIR APPLICATIONS

卷:119

Article

Magdziarz, Marcin

关键词: Subdiffusion;    Inverse subordinator;    First-passage time;    alpha-stable distribution;    Fractional Fokker-Planck equation;   

DOI  :  10.1016/j.spa.2009.05.006

来源: Elsevier

【 摘 要 】

In statistical physics, subdiffusion processes are characterized by certain power-law deviations from the classical Brownian linear time dependence of the mean square displacement. For the mathematical description Of subdiffusion, one uses fractional Fokker-Planck equations. In this paper we construct a stochastic process, whose probability density function is the solution of the fractional Fokker-Planck equation with time-dependent drift. We propose a strongly and uniformly convergent approximation scheme which allows us to approximate solutions of the fractional Fokker-Planck equation using Monte Carlo methods. The obtained results for moments of stochastic integrals driven by the inverse alpha-stable subordinator play a crucial role in the proofs, but may be also of independent interest. (C) 2009 Elsevier B.V. All rights reserved.

【 授权许可】

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