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Biased movement at a boundary and conditional occupancy times for diffusion processes

Part of: Markov processes

Published online by Cambridge University Press:  14 July 2016

Otso Ovaskainen  and
Stephen J. Cornell
Otso Ovaskainen*
Affiliation:
University of Helsinki
Stephen J. Cornell*
Affiliation:
University of Cambridge
*
∗Postal address: Department of Ecology and Systematics, PO Box 65 (Viikinkaari 1), University of Helsinki, FIN-00014, Finland. Email address: otso.ovaskainen@helsinki.fi
∗∗Postal address: Department of Zoology, University of Cambridge, Downing Street, Cambridge CB2 3EJ, UK
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Abstract

Motivated by edge behaviour reported for biological organisms, we show that random walks with a bias at a boundary lead to a discontinuous probability density across the boundary. We continue by studying more general diffusion processes with such a discontinuity across an interior boundary. We show how hitting probabilities, occupancy times and conditional occupancy times may be solved from problems that are adjoint to the original diffusion problem. We highlight our results with a biologically motivated example, where we analyze the movement behaviour of an individual in a network of habitat patches surrounded by dispersal habitat.

Keywords

Random walkbias at boundarydiffusion approximationhitting probabilityexit timeconditional exit timeoccupancy timeconditional occupancy time

MSC classification

Primary: 60J60: Diffusion processes
Secondary: 92D50: Animal behavior
Type
Research Papers
Information
Journal of Applied Probability , Volume 40 , Issue 3 , September 2003 , pp. 557 - 580
Copyright
Copyright © Applied Probability Trust 2003 

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