Limiting Approximations for Stochastic Processes in Systems Biology

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dc.contributor.advisorCox, Dennis D.en_US
dc.contributor.committeeMemberKimmel, Mareken_US
dc.contributor.committeeMemberLevine, Herberten_US
dc.creatorWoroszylo, Casperen_US
dc.date.accessioned2016-02-05T22:08:38Zen_US
dc.date.available2016-02-05T22:08:38Zen_US
dc.date.created2015-05en_US
dc.date.issued2015-04-24en_US
dc.date.submittedMay 2015en_US
dc.date.updated2016-02-05T22:08:38Zen_US
dc.description.abstractInterest in stochastic modeling of biochemical processes has increased over the past two decades due to advancements in computing power and an increased understanding of the underlying physical phenomena. The Gillespie algorithm is an exact simulation technique for reproducing sample paths from a continuous-time Markov chain. However, when spatial and temporal time scales vary within a given system, a purely stochastic approach becomes intractable. In this work, we develop two types of hybrid approximations, namely piecewise-deterministic approximations. These approaches yield strong approximations for either the entire biochemical system or a subset of the system, provided the purely stochastic system is appropriately rescaled.en_US
dc.format.mimetypeapplication/pdfen_US
dc.identifier.citationWoroszylo, Casper. "Limiting Approximations for Stochastic Processes in Systems Biology." (2015) Diss., Rice University. <a href="https://hdl.handle.net/1911/88432">https://hdl.handle.net/1911/88432</a>.en_US
dc.identifier.urihttps://hdl.handle.net/1911/88432en_US
dc.language.isoengen_US
dc.rightsCopyright is held by the author, unless otherwise indicated. Permission to reuse, publish, or reproduce the work beyond the bounds of fair use or other exemptions to copyright law must be obtained from the copyright holder.en_US
dc.subjectDensity Dependent Markov Jump Processesen_US
dc.subjectMultiscale Modelsen_US
dc.subjectPiecewise Deterministic Markov Processesen_US
dc.subjectSystems Biologyen_US
dc.titleLimiting Approximations for Stochastic Processes in Systems Biologyen_US
dc.typeThesisen_US
dc.type.materialTexten_US
thesis.degree.departmentStatisticsen_US
thesis.degree.disciplineEngineeringen_US
thesis.degree.grantorRice Universityen_US
thesis.degree.levelDoctoralen_US
thesis.degree.nameDoctor of Philosophyen_US
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