Fractional Pearson diffusions

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:403

Article

Leonenko, Nikolai N.¹  Meerschaert, Mark M.²  Sikorskii, Alla² 

[1] Cardiff Univ, Cardiff Sch Math, Cardiff CF24 4YH, S Glam, Wales

[2] Michigan State Univ, Dept Stat & Probabil, E Lansing, MI 48824 USA

关键词: Pearson diffusion;    Fractional derivative;    Eigenfunction expansion;    Stable process;    Hitting time;    Mittag-Leffler function;   

DOI  :  10.1016/j.jmaa.2013.02.046

来源: Elsevier

【 摘 要 】

Pearson diffusions are governed by diffusion equations with polynomial coefficients. Fractional Pearson diffusions are governed by the corresponding time-fractional diffusion equation. They are useful for modeling sub-diffusive phenomena, caused by particle sticking and trapping. This paper provides explicit strong solutions for fractional Pearson diffusions, using spectral methods. It also presents stochastic solutions, using a non-Markovian inverse stable time change. (C) 2013 Elsevier Inc. All rights reserved.

【 授权许可】

Free