The Smoluchowski-Kramers Approximation for Stochastic Differential Equations with Arbitrary State Dependent Friction

Persistent Link:
http://hdl.handle.net/10150/293564
Title:
The Smoluchowski-Kramers Approximation for Stochastic Differential Equations with Arbitrary State Dependent Friction
Author:
Hottovy, Scott
Issue Date:
2013
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:
In this dissertation a class of stochastic differential equations is considered in the limit as mass tends to zero, called the Smoluchowski-Kramers limit. The Smoluchowski-Kramers approximation is useful in simplifying the dynamics of a system. For example, the problems of calculating of rates of chemical reactions, describing dynamics of complex systems with noise, and measuring ultra small forces, are simplified using the Smoluchowski-Kramers approximation. In this study, we prove strong convergence in the small mass limit for a multi-dimensional system with arbitrary state-dependent friction and noise coefficients. The main result is proved using a theory of convergence of stochastic integrals developed by Kurtz and Protter. The framework of the main theorem is sufficiently arbitrary to include systems of stochastic differential equations driven by both white and Ornstein-Uhlenbeck colored noises.
Type:
text; Electronic Dissertation
Keywords:
Overdamped; Smoluchowski; State-dependent friction; Applied Mathematics; Kramers
Degree Name:
Ph.D.
Degree Level:
doctoral
Degree Program:
Graduate College; Applied Mathematics
Degree Grantor:
University of Arizona
Advisor:
Wehr, Jan

Full metadata record

DC FieldValue Language
dc.language.isoenen_US
dc.titleThe Smoluchowski-Kramers Approximation for Stochastic Differential Equations with Arbitrary State Dependent Frictionen_US
dc.creatorHottovy, Scotten_US
dc.contributor.authorHottovy, Scotten_US
dc.date.issued2013-
dc.publisherThe University of Arizona.en_US
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_US
dc.description.abstractIn this dissertation a class of stochastic differential equations is considered in the limit as mass tends to zero, called the Smoluchowski-Kramers limit. The Smoluchowski-Kramers approximation is useful in simplifying the dynamics of a system. For example, the problems of calculating of rates of chemical reactions, describing dynamics of complex systems with noise, and measuring ultra small forces, are simplified using the Smoluchowski-Kramers approximation. In this study, we prove strong convergence in the small mass limit for a multi-dimensional system with arbitrary state-dependent friction and noise coefficients. The main result is proved using a theory of convergence of stochastic integrals developed by Kurtz and Protter. The framework of the main theorem is sufficiently arbitrary to include systems of stochastic differential equations driven by both white and Ornstein-Uhlenbeck colored noises.en_US
dc.typetexten_US
dc.typeElectronic Dissertationen_US
dc.subjectOverdampeden_US
dc.subjectSmoluchowskien_US
dc.subjectState-dependent frictionen_US
dc.subjectApplied Mathematicsen_US
dc.subjectKramersen_US
thesis.degree.namePh.D.en_US
thesis.degree.leveldoctoralen_US
thesis.degree.disciplineGraduate Collegeen_US
thesis.degree.disciplineApplied Mathematicsen_US
thesis.degree.grantorUniversity of Arizonaen_US
dc.contributor.advisorWehr, Janen_US
dc.contributor.committeememberWatkins, Josephen_US
dc.contributor.committeememberKennedy, Thomasen_US
dc.contributor.committeememberSethuraman, Sunderen_US
dc.contributor.committeememberWehr, Janen_US
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