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Area and perimeter covered by anomalous diffusion processes

MPS-Authors
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Lukovic,  Mirko
Department of Nonlinear Dynamics, Max Planck Institute for Dynamics and Self-Organization, Max Planck Society;

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Geisel,  Theo
Department of Nonlinear Dynamics, Max Planck Institute for Dynamics and Self-Organization, Max Planck Society;

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Eule,  Stephan
Department of Nonlinear Dynamics, Max Planck Institute for Dynamics and Self-Organization, Max Planck Society;

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Citation

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.


Cite as: https://hdl.handle.net/11858/00-001M-0000-0029-0FD1-B
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.