Anomalous diffusion for a correlated process with long jumps

Tomasz Srokowski

Physica A: Statistical Mechanics and its Applications, 2011, vol. 390, issue 18, 3077-3085

Abstract: We discuss diffusion properties of a dynamical system, which is characterised by long-tail distributions and finite correlations. The particle velocity has the stable Lévy distribution; it is assumed as a jumping process (the kangaroo process) with a variable jumping rate. Both the exponential and the algebraic form of the covariance–defined for the truncated distribution–are considered. It is demonstrated by numerical calculations that the stationary solution of the master equation for the case of power-law correlations decays with time, but a simple modification of the process makes the tails stable. The main result of the paper is a finding that–in contrast to the velocity fluctuations–the position variance may be finite. It rises with time faster than linearly: the diffusion is anomalously enhanced. On the other hand, a process which follows from a superposition of the Ornstein–Uhlenbeck–Lévy processes always leads to position distributions with a divergent variance which means accelerated diffusion.

Keywords: Diffusion; Jumping process; Correlations; Stable Lévy distribution (search for similar items in EconPapers)
Date: 2011
References: View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:390:y:2011:i:18:p:3077-3085

DOI: 10.1016/j.physa.2011.04.022

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