Persistent Link:
http://hdl.handle.net/10150/556867
Title:
The Effects of Time Delay on Noisy Systems
Author:
McDaniel, Austin James
Issue Date:
2015
Publisher:
The University of Arizona.
Rights:
Copyright © is held by the author. Digital access to this material is made possible by the University Libraries, University of Arizona. Further transmission, reproduction or presentation (such as public display or performance) of protected items is prohibited except with permission of the author.
Abstract:
We consider a general stochastic differential delay equation (SDDE) with multiplicative colored noise. We study the limit as the time delays and the correlation times of the noises go to zero at the same rate. First, we derive the limiting equation for the equation obtained by Taylor expanding the SDDE to first order in the time delays. The limiting equation contains a noise-induced drift term that depends on the ratios of the time delays to the correlation times of the noises. We prove that, under appropriate assumptions, the solution of the equation obtained by the Taylor expansion converges to the solution of this limiting equation in probability with respect to the sup norm over compact time intervals. Next, we derive the limiting equation for the SDDE and prove a similar convergence result regarding convergence of the solution of the SDDE to the solution of this limiting equation. We see that the limiting equation corresponding to the equation obtained by the Taylor expansion is an approximation of the limiting equation corresponding to the SDDE. Finally, we study the effects of time delay on a particular model of active Brownian motion.
Type:
text; Electronic Dissertation
Keywords:
stochastic differential equations; time delay; Applied Mathematics; stochastic differential delay equations
Degree Name:
Ph.D.
Degree Level:
doctoral
Degree Program:
Graduate College; Applied Mathematics
Degree Grantor:
University of Arizona
Advisor:
Wehr, Janek

Full metadata record

DC FieldValue Language
dc.language.isoen_USen
dc.titleThe Effects of Time Delay on Noisy Systemsen_US
dc.creatorMcDaniel, Austin Jamesen
dc.contributor.authorMcDaniel, Austin Jamesen
dc.date.issued2015en
dc.publisherThe University of Arizona.en
dc.rightsCopyright © is held by the author. Digital access to this material is made possible by the University Libraries, University of Arizona. Further transmission, reproduction or presentation (such as public display or performance) of protected items is prohibited except with permission of the author.en
dc.description.abstractWe consider a general stochastic differential delay equation (SDDE) with multiplicative colored noise. We study the limit as the time delays and the correlation times of the noises go to zero at the same rate. First, we derive the limiting equation for the equation obtained by Taylor expanding the SDDE to first order in the time delays. The limiting equation contains a noise-induced drift term that depends on the ratios of the time delays to the correlation times of the noises. We prove that, under appropriate assumptions, the solution of the equation obtained by the Taylor expansion converges to the solution of this limiting equation in probability with respect to the sup norm over compact time intervals. Next, we derive the limiting equation for the SDDE and prove a similar convergence result regarding convergence of the solution of the SDDE to the solution of this limiting equation. We see that the limiting equation corresponding to the equation obtained by the Taylor expansion is an approximation of the limiting equation corresponding to the SDDE. Finally, we study the effects of time delay on a particular model of active Brownian motion.en
dc.typetexten
dc.typeElectronic Dissertationen
dc.subjectstochastic differential equationsen
dc.subjecttime delayen
dc.subjectApplied Mathematicsen
dc.subjectstochastic differential delay equationsen
thesis.degree.namePh.D.en
thesis.degree.leveldoctoralen
thesis.degree.disciplineGraduate Collegeen
thesis.degree.disciplineApplied Mathematicsen
thesis.degree.grantorUniversity of Arizonaen
dc.contributor.advisorWehr, Janeken
dc.contributor.committeememberWehr, Janeken
dc.contributor.committeememberKennedy, Tomen
dc.contributor.committeememberSethuraman, Sunderen
dc.contributor.committeememberErcolani, Nicken
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