The exit-time problem for a Markov jump process

Burch, N.; D'Elia, Marta; Lehoucq, Richard B.

doi:10.1140/epjst/e2014-02331-7

Title: The exit-time problem for a Markov jump process

Journal Article · Mon Dec 15 00:00:00 EST 2014 · European Physical Journal. A

DOI:https://doi.org/10.1140/epjst/e2014-02331-7· OSTI ID:1235248

Burch, N. ^[1]; D'Elia, Marta ^[2]; Lehoucq, Richard B. ^[2]

Gonzaga Univ., Spokane, WA (United States)
Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)

The purpose of our 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. 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. Furthermore, this calculus allows us to pose nonlocal backward and forward Kolmogorov equations, the former equation granting the various moments of the exit-time distribution.

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Research Organization:: Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)

Sponsoring Organization:: USDOE National Nuclear Security Administration (NNSA)

DOE Contract Number:: AC04-94AL85000

OSTI ID:: 1235248

Report Number(s):: SAND2015-0850J; 563489

Journal Information:: European Physical Journal. A, Vol. 223; ISSN 1434-6001

Publisher:: Springer

Country of Publication:: United States

Language:: English

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