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Discrete Models for Scattering Populations

Part of: Waves Stochastic systems and control

Published online by Cambridge University Press:  14 July 2016

Patrick Fayard  and
Timothy R. Field
Patrick Fayard*
Affiliation:
McMaster University
Timothy R. Field*
Affiliation:
McMaster University
*
∗Postal address: Department of Electrical and Computer Engineering, McMaster University, 1280 Main Street West, Hamilton, Ontario L8S 4K1, Canada.
∗Postal address: Department of Electrical and Computer Engineering, McMaster University, 1280 Main Street West, Hamilton, Ontario L8S 4K1, Canada.
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Abstract

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Jakeman's random walk model with step number fluctuations describes the coherent amplitude scattered from a rough medium in terms of the summation of individual scatterers' contributions. If the scattering population conforms to a birth-death immigration model, the resulting amplitude is K-distributed. In this context, we derive a class of diffusion processes as an extension of the ordinary birth-death immigration model. We show how this class encompasses four different cross-section models commonly studied in the literature. We conclude by discussing the advantages of this unified description.

Keywords

Stochastic differential equationscattering of wavesK-distributionFokker-Planck equationpopulation dynamicsdiffusion process

MSC classification

Secondary: 74J20: Wave scattering 93E03: Stochastic systems, general
Type
Research Article
Information
Journal of Applied Probability , Volume 48 , Issue 1 , March 2011 , pp. 285 - 292
Copyright
Copyright © Applied Probability Trust 2011 

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