Computing the exit-time for a finite-range symmetric jump process

Burch Nathanial () and Lehoucq R. B. ()
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Burch Nathanial: Department of Mathematics, Gonzaga University, 502 E. Boone Ave. MSC 2615, Spokane, WA 99258, USA
Lehoucq R. B.: Sandia National Laboratories, P.O. Box 5800, MS 1320, Albuquerque, NM 87185–1320, USA

Monte Carlo Methods and Applications, 2015, vol. 21, issue 2, 139-152

Abstract: This paper investigates the exit-time for a broad class of symmetric finite-range jump processes via the corresponding master equation, a nonlocal diffusion equation suitably constrained. In direct analogy to the classical diffusion equation with a homogeneous Dirichlet boundary condition, the nonlocal diffusion equation is augmented with a homogeneous volume-constraint. The volume-constrained master equation provides an efficient alternative over Monte Carlo simulation for computing an important statistic of the process. Several numerical examples are given.

Keywords: Nonlocal diffusion; jump process; random walks; anomalous diffusion; volume-constraints; exit-time; first-passage (search for similar items in EconPapers)
Date: 2015
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DOI: 10.1515/mcma-2014-0015

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