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DOE OSTI · 1497664

The exit-time problem for a Markov jump process

Lehoucq, Richard B.·D'Elia, Marta·Burch, Nathanial
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Abstract

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.

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71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS97 MATHEMATICS AND COMPUTINGBrownian MotionEuropean Physical Journal Special TopicJump ProcessSandia National LaboratoryVolume Constraint

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Lehoucq, Richard B., D'Elia, Marta, Burch, Nathanial. 2014-12-15. The exit-time problem for a Markov jump process. https://doi.org/10.1140/epjst%2Fe2014-02331-7

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