The Tree-Grid method is a novel explicit convergent scheme for solving stochastic control problems or Hamilton-Jacobi-Bellman equations with one space dimension. One of the characteristics of the scheme is that the stencil size is dependent on space, control and possibly also on time. Because of the dependence on the control variable, it is not trivial to solve the optimization problem inside the method. Recently, this optimization part was solved by brute-force testing of all permitted controls....

The purpose of the present article is to compare different phase-space sampling methods, such as purely stochastic methods (Rejection method, Metropolized independence sampler, Importance Sampling), stochastically perturbed Molecular Dynamics methods (Hybrid Monte Carlo, Langevin Dynamics, Biased Random Walk), and purely deterministic methods (Nosé-Hoover chains, Nosé-Poincaré and Recursive Multiple Thermostats (RMT) methods). After recalling some theoretical convergence properties for the...

Many complex systems occurring in various application share the property that the underlying Markov process remains in certain regions of the state space for long times, and that transitions between such metastable sets occur only rarely. Often the dynamics within each metastable set is of minor importance, but the transitions between these sets are crucial for the behavior and the understanding of the system. Since simulations of the original process are usually prohibitively expensive, the effective...