2026-09-20T06:56:28Z https://www.ideals.illinois.edu/oai-pmh

oai:www.ideals.illinois.edu:2142/26067 2023-07-10 col_2142_5131 col_2142_14787 com_2142_5130 com_2142_9630 com_2142_234

West, Matthew Dullerud, Geir E. Maginnis, Peter A. 2011-08-25T22:11:39Z 2011-08-25T22:11:39Z 2011-08-25T22:11:39Z 2011-08 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. Item withdrawn by Alexis Thompson (athmpsn1@illinois.edu) on 2011-07-15T16:20:17Z Item was in collections: University of Illinois Theses & Dissertations (ID: 1) No. of bitstreams: 1 maginnis_peter.pdf: 345756 bytes, checksum: 395514d37baa3b8be82319e3b04f1aa5 (MD5) Made available in DSpace on 2011-08-25T22:11:39Z (GMT). No. of bitstreams: 2 maginnis_peter.pdf: 345937 bytes, checksum: b12863aee69a0b3856e353286340bf7f (MD5) license.txt: 4064 bytes, checksum: e2f5a71cda3f63ebbb356d76026533ce (MD5) http://hdl.handle.net/2142/26067 en Copyright 2011 Peter A. Maginnis variance reduction Poisson tau-leaping antithetical stratified mean estimation Variance reduction for Poisson and Markov jump processes Mechanical Sci & Engineering 1917 Mechanical Engineering 0133 University of Illinois at Urbana-Champaign Thesis M.S. MS:Mechanical Engineerng -UIUC 10KS0133MS