Limiting Approximations for Stochastic Processes in Systems Biology

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dc.contributor.advisorCox, Dennis D.
dc.contributor.committeeMemberKimmel, Marek
dc.contributor.committeeMemberLevine, Herbert
dc.creatorWoroszylo, Casper
dc.date.accessioned2016-02-05T22:08:38Z
dc.date.available2016-02-05T22:08:38Z
dc.date.created2015-05
dc.date.issued2015-04-24
dc.date.submittedMay 2015
dc.date.updated2016-02-05T22:08:38Z
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.
dc.format.mimetypeapplication/pdf
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>.
dc.identifier.urihttps://hdl.handle.net/1911/88432
dc.language.isoeng
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.
dc.subjectDensity Dependent Markov Jump Processes
dc.subjectMultiscale Models
dc.subjectPiecewise Deterministic Markov Processes
dc.subjectSystems Biology
dc.titleLimiting Approximations for Stochastic Processes in Systems Biology
dc.typeThesis
dc.type.materialText
thesis.degree.departmentStatistics
thesis.degree.disciplineEngineering
thesis.degree.grantorRice University
thesis.degree.levelDoctoral
thesis.degree.nameDoctor of Philosophy
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