Communications in Mathematical Sciences
Volume 9 (2011)
A structure-preserving numerical discretization of reversible diffusions
Pages: 1051 – 1072
We propose a numerical discretization scheme for the infinitesimal generator of a diffusion process based on a finite volume approximation. The resulting discrete-space operator can be interpreted as a jump process on the mesh whose invariant distribution is precisely the cell approximation of the Boltzmann invariant measure and preserves the detailed balance property of the original stochastic process. Moreover this approximation is robust in the sense that these properties remain valid independently of the grid size.
reversible diffusions, finite-volume method, detailed balance, coarse-graining
2010 Mathematics Subject Classification
60G10, 60H35, 60J27, 65N08