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  Area and perimeter covered by anomalous diffusion processes

Lukovic, M., Geisel, T., & Eule, S. (2013). Area and perimeter covered by anomalous diffusion processes. New Journal of Physics, 15: 063034. doi:10.1088/1367-2630/15/6/063034.

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Item Permalink: http://hdl.handle.net/11858/00-001M-0000-0029-0FD1-B Version Permalink: http://hdl.handle.net/11858/00-001M-0000-0029-0FD2-9
Genre: Journal Article

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 Creators:
Lukovic, Mirko1, Author              
Geisel, Theo1, Author              
Eule, Stephan1, Author              
Affiliations:
1Department of Nonlinear Dynamics, Max Planck Institute for Dynamics and Self-Organization, Max Planck Society, ou_2063286              

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 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.

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Language(s): eng - English
 Dates: 2013-06-21
 Publication Status: Published in print
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 Rev. Method: Peer
 Identifiers: eDoc: 673697
DOI: 10.1088/1367-2630/15/6/063034
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Title: New Journal of Physics
Source Genre: Journal
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Pages: - Volume / Issue: 15 Sequence Number: 063034 Start / End Page: - Identifier: -