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Area and perimeter covered by anomalous diffusion processes.

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Bibliographic Details
Title: Area and perimeter covered by anomalous diffusion processes.
Authors: Lukovi´c, Mirko1,2 lukovic@nld.ds.mpg.de, Geisel, Theo1,2, Eule, Stephan1
Source: New Journal of Physics. 2013, Vol. 15 Issue 6, p1-11. 11p.
Subjects: Diffusion processes, Random walks, Stochastic processes, Foraging behavior, Sea birds, Brownian motion
Abstract: We investigate the geometric properties of two-dimensional continuous time random walks that are used extensively to model stochastic processes exhibiting anomalous diffusion in a variety of different fields. Using the concept of subordination, we determine exact analytical expressions for the average perimeter and area of the convex hulls for this class of non-Markovian processes. As the convex hull is a simple measure to estimate the home range of animals, our results give analytical estimates for the home range of foraging animals that perform sub-diffusive search strategies such as some Mediterranean seabirds and animals that ambush their prey. We also apply our results to Levy flights where possible. [ABSTRACT FROM AUTHOR]
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Database: Engineering Source
Description
Abstract:We investigate the geometric properties of two-dimensional continuous time random walks that are used extensively to model stochastic processes exhibiting anomalous diffusion in a variety of different fields. Using the concept of subordination, we determine exact analytical expressions for the average perimeter and area of the convex hulls for this class of non-Markovian processes. As the convex hull is a simple measure to estimate the home range of animals, our results give analytical estimates for the home range of foraging animals that perform sub-diffusive search strategies such as some Mediterranean seabirds and animals that ambush their prey. We also apply our results to Levy flights where possible. [ABSTRACT FROM AUTHOR]
ISSN:13672630
DOI:10.1088/1367-2630/15/6/063034