Markovian Multigrid Discretization

Abstract:

Many interesting property properties of Markov processes are encoded in the transfer operator that is the solution operator of the underlying Fokker-Planck equation. On the other hand, for computational treatment a finite dimensional approximation of this operator is essential. We will present a novel Galerkin method that is based on a multigrid discretization of the state space of the process. Moreover, we will discuss properties of the approach that are desired for multigrid methods, in general, but usually difficult to guarantee.