Communications in Mathematical Sciences

Volume 9 (2011)

Number 4

A structure-preserving numerical discretization of reversible diffusions

Pages: 1051 – 1072

DOI: https://dx.doi.org/10.4310/CMS.2011.v9.n4.a6

Authors

Carsten Hartmann (Freie Universität Berlin, Institut für Mathematik, Berlin, Germany)

Juan C. Latorre (Freie Universität Berlin, Institut für Mathematik, Berlin, Germany)

Philipp Metzner (Freie Universität Berlin, Institut für Mathematik, Berlin, Germany)

Christof Schütte (Freie Universität Berlin, Institut für Mathematik, Berlin, Germany)

Abstract

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.

Keywords

reversible diffusions, finite-volume method, detailed balance, coarse-graining

2010 Mathematics Subject Classification

60G10, 60H35, 60J27, 65N08

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Published 29 July 2011