In A Relative Value Iteration Algorithm for Nondegenerate Controlled Diffusions, [SIAM J. Control Optim., 50 (2012), pp. 1886–1902], convergence of the relative value iteration for the ergodic control problem for a nondegenerate diffusion controlled through its drift was established, under the assumption of geometric ergodicity, using two methods: (a) the theory of monotone dynamical systems an...

We provide a rather general perfection result for crude local semi-flows taking values in Polish space showing that semi-flow has modification which is (perfect) invariant under suitable metric dynamical system. Such (local) induces random system (RDS). Then we show this can be applied to several classes of stochastic differential equations driven by semimartingales with stationary increments s...

In order to ensure convergence to the viscosity solution, the standard method for discretizing HJB PDEs uses forward/backward differencing for the drift term. In this paper, we devise a monotone method which uses central weighting as much as possible. In order to solve the discretized algebraic equations, we have to maximize a possibly discontinuous objective function at each node. Nevertheless...

A process associated with integrated Brownian motion is introduced that characterizes the limit behavior of nonparametric least squares and maximum likelihood estimators of convex functions and convex densities, respectively. We call this process “the invelope” and show that it is an almost surely uniquely defined function of integrated Brownian motion. Its role is comparable to the role of the...

In A Relative Value Iteration Algorithm for Nondegenerate Controlled Diffusions, [SIAM J. Control Optim., 50 (2012), pp. 1886–1902], convergence of the relative value iteration for the ergodic control problem for a nondegenerate diffusion controlled through its drift was established, under the assumption of geometric ergodicity, using two methods: (a) the theory of monotone dynamical systems an...

Abstract. The ergodic control problem for a non-degenerate controlled diffusion controlled through its drift is considered under a uniform stability condition that ensures the well-posedness of the associated Hamilton–Jacobi– Bellman (HJB) equation. A nonlinear parabolic evolution equation is then proposed as a continuous time continuous state space analog of White’s ‘relative value iteration’ ...

A parallel dynamic load balancing for 2-D and 3-D semiconductor device simulations is proposed. The hydrodynamic and drift diffusion models are discretized and solved with finite volume (box) and monotone iterative methods. Dynamic load balancing for parallel domain decomposition as well as parallel I-V point simulations are demonstrated to be efficient methods for multidimensional device simul...

Kinetic transport equations with a given confining potential and non-linear relaxation type collision operators are considered. General (monotone) energy dependent equilibrium distributions are allowed with a chemical potential ensuring mass conservation. Existence and uniqueness of solutions is proven for initial data bounded by equilibrium distributions. The diffusive macroscopic limit is car...