Cox, Dennis D.2016-02-052016-02-052015-052015-04-24May 2015Woroszylo, 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>.https://hdl.handle.net/1911/88432Interest 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.application/pdfengCopyright 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.Density Dependent Markov Jump ProcessesMultiscale ModelsPiecewise Deterministic Markov ProcessesSystems BiologyThesis2016-02-05