University of Illinois Urbana-Champaign

Variance reduction for Poisson and Markov jump processes

Maginnis, Peter A.

Content Files
maginnis_peter.pdf

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https://hdl.handle.net/2142/26067

Description

Title
Variance reduction for Poisson and Markov jump processes
Author(s)
Maginnis, Peter A.
Issue Date
2011-08-25T22:11:39Z
Director of Research (if dissertation) or Advisor (if thesis)
  • West, Matthew
  • Dullerud, Geir E.
Department of Study
Mechanical Sci & Engineering
Discipline
Mechanical Engineering
Degree Granting Institution
University of Illinois at Urbana-Champaign
Degree Name
M.S.
Degree Level
Thesis
Date of Ingest
2011-08-25T22:11:39Z
Keyword(s)
  • variance reduction
  • Poisson
  • tau-leaping
  • antithetical
  • stratified
  • mean estimation
Abstract
This thesis develops new variance reduction algorithms for the simulation and estimation of stochastic dynamic models. It provides particular application to particle dynamics models including an emissions process and radioactive decay. These algorithms apply several variance reduction techniques to the generation of Poisson variates in the tau-leaping time-stepping method for Markov processes. Both antithetical and stratified sampling variance-reduction techniques are considered for Poisson mean estimation, and a hybridization of them is developed that has lower variance than either for every value of the Poisson parameter. Several analytical characterizations of estimator variance are proven for different Poisson parameter regimes. By applying these variance-reduced Poisson mean estimation techniques in an appropriate dynamic fashion to the tau-leaping method, variance-reduced pathwise mean estimators are generated for stochastic Markov processes. It is numerically demonstrated that stepwise variance reduction produces pathwise variance reduction in estimators of systems of physical interest.
Graduation Semester
2011-08
Permalink
http://hdl.handle.net/2142/26067
Copyright and License Information
Copyright 2011 Peter A. Maginnis

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