Fractional Fokker-Planck Equation with Space and Time Dependent Drift and Diffusion

被引：12

作者：

Lv, Longjin ^{[1
]}

Qiu, Weiyuan ^{[2
]}

Ren, Fuyao ^{[2
]}

机构：

[1] Zhejiang Univ, Ningbo Inst Technol, Dept Informat Sci & Engn, Ningbo 315000, Zhejiang, Peoples R China

[2] Fudan Univ, Dept Math, Shanghai 200433, Peoples R China

来源：

JOURNAL OF STATISTICAL PHYSICS | 2012年 / 149卷 / 04期

关键词：

Anomalous diffusion equation; Subordinated process; Stochastic representation; Numerical approximation; ANOMALOUS DIFFUSION; LEVY FLIGHTS; DYNAMICS;

D O I：

10.1007/s10955-012-0618-3

中图分类号：

O4 [物理学];

学科分类号：

0702 ;

摘要：

In this paper, we aim to answer the question proposed by Magdziarz (Stoch. Proc. Appl. 119:3238-3252, 2009), i.e. we investigate the solution of an anomalous diffusion equation with time and space dependent force and diffusion coefficient. First, we try to find the stochastic representation of this equation, which means the PDF of this stochastic process is rightly the solution of the equation we aim to solve. Then, we also simulate the sample paths of the stochastic process. At last, taking advantage of the stochastic representation method, we employed Monte Carlo method to approximate the solution of the mentioned equation.

引用

页码：619 / 628

页数：10

共 25 条

[1]

[Anonymous], 1994, LEVY FLIGHTS RELATED

[2] SUBRECOIL LASER COOLING AND LEVY FLIGHTS [J].

BARDOU, F ;

BOUCHAUD, JP ;

EMILE, O ;

ASPECT, A ;

COHENTANNOUDJI, C .

PHYSICAL REVIEW LETTERS, 1994, 72 (02) :203-206

[3] Microscopic dynamics of the nonlinear Fokker-Planck equation: A phenomenological model [J].

Borland, L .

PHYSICAL REVIEW E, 1998, 57 (06) :6634-6642

[4] ANOMALOUS DIFFUSION IN ELONGATED MICELLES AND ITS LEVY FLIGHT INTERPRETATION [J].

BOUCHAUD, JP ;

OTT, A ;

LANGEVIN, D ;

URBACH, W .

JOURNAL DE PHYSIQUE II, 1991, 1 (12) :1465-1482

[5]

Bouchaud P., 1990, PHYS REP, P127

[6] Fractional Fokker-Planck equation with tempered α-stable waiting times: Langevin picture and computer simulation [J].

Gajda, Janusz ;

Magdziarz, Marcin .

PHYSICAL REVIEW E, 2010, 82 (01)

[7] Use and abuse of a fractional Fokker-Planck dynamics for time-dependent driving [J].

Heinsalu, E. ;

Patriarca, M. ;

Goychuk, I. ;

Haenggi, P. .

PHYSICAL REVIEW LETTERS, 2007, 99 (12)

[8] Fractional Fokker-Planck Equations for Subdiffusion with Space- and Time-Dependent Forces [J].

Henry, B. I. ;

Langlands, T. A. M. ;

Straka, P. .

PHYSICAL REVIEW LETTERS, 2010, 105 (17)

[9]

Janicki A., 1994, Simulation and Chaotic Behavior of ?-Stable Stochastic Processes

[10] Solutions for a generalized fractional anomalous diffusion equation [J].

Lv, Long-Jin ;

Xiao, Jian-Bin ;

Zhang, Lin ;

Gao, Lei .

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 2009, 225 (01) :301-308

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