We show that Markov couplings can be used to improve the accuracy of Markov chain Monte Carlo calculations in some situations where the steady-state probability distribution is not explicitly known. The technique generalizes the notion of control variates from classical Monte Carlo integration. We illustrate it using two models of nonequilibrium transport.
We use a geometric approach, similar to van Leer's MUSCL schemes, to construct a second-order accurate generalization of Godunov's method for solving scalar conservation laws. By making suitable approximations we obtain a scheme which is easy to implement and total variation diminishing. We also investigate the entropy condition from the standpoint of the… (More)
All Rights Reserved 2000 ii For my parents iv Acknowledgements I am very grateful to my advisor, Professor Jonathan Goodman, who did a great job in helping me to find a lot of directions (including directions for mesh refinement, financial help, job). It has been a very enjoyable experience to work and learn from Jonathan. Thanks to Professor Olof Widlund… (More)