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    Limiting Approximations for Stochastic Processes in Systems Biology

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    Author
    Woroszylo, Casper
    Date
    2015-04-24
    Advisor
    Cox, Dennis D.
    Degree
    Doctor of Philosophy
    Abstract
    Interest 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.
    Keyword
    Density Dependent Markov Jump Processes; Multiscale Models; Piecewise Deterministic Markov Processes; Systems Biology
    Citation
    Woroszylo, Casper. "Limiting Approximations for Stochastic Processes in Systems Biology." (2015) PhD diss., Rice University. http://hdl.handle.net/1911/88432.
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    Managed by the Digital Scholarship Services at Fondren Library, Rice University
    Physical Address: 6100 Main Street, Houston, Texas 77005
    Mailing Address: MS-44, P.O.BOX 1892, Houston, Texas 77251-1892