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BROWNIAN MOTION MINUS THE INDEPENDENT INCREMENTS: REPRESENTATION AND QUEUING APPLICATION

Published online by Cambridge University Press:  21 July 2020

Kerry Fendick Open the ORCID record for Kerry Fendick [Opens in a new window]
Kerry Fendick*
Affiliation:
Applied Physics Laboratory, 11100 Johns Hopkins Road, Laurel, MD20723, USA E-mail: kerry.fendick@jhuapl.edu
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Abstract

This paper relaxes assumptions defining multivariate Brownian motion (BM) to construct processes with dependent increments as tractable models for problems in engineering and management science. We show that any Gaussian Markov process starting at zero and possessing stationary increments and a symmetric smooth kernel has a parametric kernel of a particular form, and we derive the unique unbiased, jointly sufficient, maximum-likelihood estimators of those parameters. As an application, we model a single-server queue driven by such a process and derive its transient distribution conditional on its history.

Keywords

Gaussian fluid queueGaussian Markov processmultivariate Brownian bridgemultivariate Brownian motionregulated Brownian motionstationary increments
Type
Research Article
Information
Probability in the Engineering and Informational Sciences , Volume 36 , Issue 1 , January 2022 , pp. 144 - 168
Copyright
Copyright © The Author(s), 2020. Published by Cambridge University Press

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