Non-Markovian diffusion equations and processes: analysis and simulations

Autor:	Mura, Antonio, Taqqu, Murad S., Mainardi, Francesco
Rok vydání:	2007
Předmět:	Mathematical Physics Condensed Matter - Statistical Mechanics Mathematics - Probability Physics - Data Analysis Statistics and Probability 6A33 33E12 44A10 33C60 45K05 60G18
Druh dokumentu:	Working Paper
DOI:	10.1016/j.physa.2008.04.035
Popis:	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. Comment: 43 pages, 19 figures, in press on Physica A (2008)
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/0712.0240 Zobrazit plný text záznamu View this record from Arxiv