Fokker-Planck type equations associated with fractional Brownian motion controlled by infinitely divisible processes

被引：20
作者：
Gajda, Janusz [1 ]
Wylomanska, Agnieszka [1 ]
机构：
[1] Wroclaw Univ Technol, Inst Math & Comp Sci, Hugo Steinhaus Ctr, PL-50370 Wroclaw, Poland
来源：
PHYSICA A-STATISTICAL MECHANICS AND ITS APPLICATIONS | 2014年 / 405卷
关键词：
Subordination; Fractional Brownian motion; Fokker-Planck equations; Accelerating-subdiffusion; ANOMALOUS DIFFUSION; LEVY FLIGHTS; SUBDIFFUSION; DYNAMICS; DRIVEN; MODELS;
D O I：
10.1016/j.physa.2014.03.016
中图分类号：
O4 [物理学];
学科分类号：
0702 ;
摘要：
In this paper we study the anomalous diffusion process driven by fractional Brownian motion delayed by general infinitely divisible subordinator. We show the analyzed process is the stochastic representation of the Fokker-Planck type equation that describes the probability density function of an introduced model. Moreover, we study main characteristics of the examined process, the first two moments, that allow us in special cases for classification of it as a system with accelerating-subdiffusion property. (C) 2014 Elsevier B.V. All rights reserved.
引用
收藏
页码：104 / 113
页数：10
相关论文
共 46 条
  • [1] Abate J., 2000, Computational probability, P257, DOI [DOI 10.1007/978-1-4757-4828-4_8, 10.1007/978-1-4757-4828-48, DOI 10.1007/978-1-4757-4828-48]
  • [2] [Anonymous], 1992, The Fokker-Planck Equation, DOI DOI 10.1007/978-3-642-61544-3_4
  • [3] CONDITIONAL LIMIT THEOREMS FOR REGULATED FRACTIONAL BROWNIAN MOTION
    Awad, Hernan
    Glynn, Peter
    [J]. ANNALS OF APPLIED PROBABILITY, 2009, 19 (06) : 2102 - 2136
  • [4] Operators associated with a stochastic differential equation driven by fractional Brownian motions
    Baudoin, Fabrice
    Coutin, Laure
    [J]. STOCHASTIC PROCESSES AND THEIR APPLICATIONS, 2007, 117 (05) : 550 - 574
  • [5] Scintillations and Levy flights through the interstellar medium
    Boldyrev, S
    Gwinn, C
    [J]. ASTROPHYSICAL JOURNAL, 2003, 584 (02) : 791 - 796
  • [6] Levy flights in external force fields: from models to equations
    Brockmann, D
    Sokolov, IM
    [J]. CHEMICAL PHYSICS, 2002, 284 (1-2) : 409 - 421
  • [7] Transient Anomalous Diffusion of Telomeres in the Nucleus of Mammalian Cells
    Bronstein, I.
    Israel, Y.
    Kepten, E.
    Mai, S.
    Shav-Tal, Y.
    Barkai, E.
    Garini, Y.
    [J]. PHYSICAL REVIEW LETTERS, 2009, 103 (01)
  • [8] Universal Algorithm for Identification of Fractional Brownian Motion. A Case of Telomere Subdiffusion
    Burnecki, Krzysztof
    Kepten, Eldad
    Janczura, Joanna
    Bronshtein, Irena
    Garini, Yuval
    Weron, Aleksander
    [J]. BIOPHYSICAL JOURNAL, 2012, 103 (09) : 1839 - 1847
  • [9] Levy flights in the Landau-Teller model of molecular collisions
    Carati, A
    Galgani, L
    Pozzi, B
    [J]. PHYSICAL REVIEW LETTERS, 2003, 90 (01) : 4
  • [10] Generalized fractional diffusion equations for accelerating subdiffusion and truncated Levy flights
    Chechkin, A. V.
    Gonchar, V. Yu.
    Gorenflo, R.
    Korabel, N.
    Sokolov, I. M.
    [J]. PHYSICAL REVIEW E, 2008, 78 (02)
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