Stochastic perturbation of the Lighthill–Whitham–Richards model via the method of stochastic characteristics

Abstract In this paper we apply the method of stochastic characteristics to a Lighthill–Whitham–Richards model. The stochastic perturbation can be seen as errors in measurement of the traffic density. For concrete examples we solve the equation perturbed by a standard Brownian motion and the geometr...

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Main Authors:	Nora Müller, Wolfgang Bock
Format:	Article
Language:	English
Published:	SpringerOpen 2021-05-01
Series:	Journal of Mathematics in Industry
Subjects:	Method of stochastic characteristics Lighthill–Whitham–Richards model Explicit solutions
Online Access:	https://doi.org/10.1186/s13362-021-00103-w

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spelling	doaj-7a0ad38899e7480d826756b6b95457852021-05-09T11:19:43ZengSpringerOpenJournal of Mathematics in Industry2190-59832021-05-0111111310.1186/s13362-021-00103-wStochastic perturbation of the Lighthill–Whitham–Richards model via the method of stochastic characteristicsNora Müller0Wolfgang Bock1Fakultät für Mathematik, Bielefeld UniversityTechnomathematics Group, Technische Universität KaiserslauternAbstract In this paper we apply the method of stochastic characteristics to a Lighthill–Whitham–Richards model. The stochastic perturbation can be seen as errors in measurement of the traffic density. For concrete examples we solve the equation perturbed by a standard Brownian motion and the geometric Brownian motion without drift.https://doi.org/10.1186/s13362-021-00103-wMethod of stochastic characteristicsLighthill–Whitham–Richards modelExplicit solutions
collection	DOAJ
language	English
format	Article
sources	DOAJ
author	Nora Müller Wolfgang Bock
spellingShingle	Nora Müller Wolfgang Bock Stochastic perturbation of the Lighthill–Whitham–Richards model via the method of stochastic characteristics Journal of Mathematics in Industry Method of stochastic characteristics Lighthill–Whitham–Richards model Explicit solutions
author_facet	Nora Müller Wolfgang Bock
author_sort	Nora Müller
title	Stochastic perturbation of the Lighthill–Whitham–Richards model via the method of stochastic characteristics
title_short	Stochastic perturbation of the Lighthill–Whitham–Richards model via the method of stochastic characteristics
title_full	Stochastic perturbation of the Lighthill–Whitham–Richards model via the method of stochastic characteristics
title_fullStr	Stochastic perturbation of the Lighthill–Whitham–Richards model via the method of stochastic characteristics
title_full_unstemmed	Stochastic perturbation of the Lighthill–Whitham–Richards model via the method of stochastic characteristics
title_sort	stochastic perturbation of the lighthill–whitham–richards model via the method of stochastic characteristics
publisher	SpringerOpen
series	Journal of Mathematics in Industry
issn	2190-5983
publishDate	2021-05-01
description	Abstract In this paper we apply the method of stochastic characteristics to a Lighthill–Whitham–Richards model. The stochastic perturbation can be seen as errors in measurement of the traffic density. For concrete examples we solve the equation perturbed by a standard Brownian motion and the geometric Brownian motion without drift.
topic	Method of stochastic characteristics Lighthill–Whitham–Richards model Explicit solutions
url	https://doi.org/10.1186/s13362-021-00103-w
work_keys_str_mv	AT noramuller stochasticperturbationofthelighthillwhithamrichardsmodelviathemethodofstochasticcharacteristics AT wolfgangbock stochasticperturbationofthelighthillwhithamrichardsmodelviathemethodofstochasticcharacteristics
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Stochastic perturbation of the Lighthill–Whitham–Richards model via the method of stochastic characteristics

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