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The exit-time problem for a Markov jump process

Journal Article · · European Physical Journal. Special Topics
 [1];  [2];  [2]
  1. Gonzaga University, Spokane, WA (United States)
  2. Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)
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The purpose of this paper is to consider the exit-time problem for a finite-range Markov jump process, i.e, the distance the particle can jump is bounded independent of its location. Additionally, such jump diffusions are expedient models for anomalous transport exhibiting super-diffusion or nonstandard normal diffusion. We refer to the associated deterministic equation as a volume-constrained nonlocal diffusion equation. The volume constraint is the nonlocal analogue of a boundary condition necessary to demonstrate that the nonlocal diffusion equation is well-posed and is consistent with the jump process. A critical aspect of the analysis is a variational formulation and a recently developed nonlocal vector calculus. Finally, this calculus allows us to pose nonlocal backward and forward Kolmogorov equations, the former equation granting the various moments of the exit-time distribution.
Research Organization:
Sandia National Laboratories (SNL-NM), Albuquerque, NM (United States)
Sponsoring Organization:
USDOE
Grant/Contract Number:
AC04-94AL85000
OSTI ID:
1497664
Alternate ID(s):
OSTI ID: 1235248
Report Number(s):
SAND--2014-16434J; 672039
Journal Information:
European Physical Journal. Special Topics, Journal Name: European Physical Journal. Special Topics Journal Issue: 14 Vol. 223; ISSN 1951-6355
Publisher:
SpringerCopyright Statement
Country of Publication:
United States
Language:
English

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Figures / Tables (7)

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Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
97 MATHEMATICS AND COMPUTING
Brownian Motion
European Physical Journal Special Topic
Jump Process
Sandia National Laboratory
Volume Constraint