Variance reduction for Poisson and Markov jump processes

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