Non-Markovian diffusion equations and processes: Analysis and simulations

A. Mura, M.S. Taqqu and F. Mainardi

Physica A: Statistical Mechanics and its Applications, 2008, vol. 387, issue 21, 5033-5064

Abstract: In this paper we introduce and analyze a class of diffusion type equations related to certain non-Markovian stochastic processes. We start from the forward drift equation which is made non-local in time by the introduction of a suitable chosen memory kernel K(t). The resulting non-Markovian equation can be interpreted in a natural way as the evolution equation of the marginal density function of a random time process l(t). We then consider the subordinated process Y(t)=X(l(t)) where X(t) is a Markovian diffusion. The corresponding time evolution of the marginal density function of Y(t) is governed by a non-Markovian Fokker–Planck equation which involves the memory kernel K(t). We develop several applications and derive the exact solutions. We consider different stochastic models for the given equations providing path simulations.

Keywords: Non-Markovian processes; Fractional derivatives; Anomalous diffusion; Subordination; Fractional Brownian motion (search for similar items in EconPapers)
Date: 2008
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (6)

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0378437108004019
Full text for ScienceDirect subscribers only. Journal offers the option of making the article available online on Science direct for a fee of $3,000

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:387:y:2008:i:21:p:5033-5064

DOI: 10.1016/j.physa.2008.04.035

Access Statistics for this article

Physica A: Statistical Mechanics and its Applications is currently edited by K. A. Dawson, J. O. Indekeu, H.E. Stanley and C. Tsallis

More articles in Physica A: Statistical Mechanics and its Applications from Elsevier
Bibliographic data for series maintained by Catherine Liu ().