Nonlocal Convection-Diffusion Problems on Bounded Domains and Finite-Range Jump Processes

作者：D%apos; Elia Marta; Du Qiang; Gunzburger Max; Lehoucq Richard

来源：Computational Methods in Applied Mathematics, 2017, 17(4): 707-722.

DOI：10.1515/cmam-2017-0029

• Nonlocal Diffusion
• Nonlocal Operators
• Nonlocal Vector Calculus
• Variational Forms
• Master Equation
• Markov Processes
• Levy Processes

A nonlocal convection-diffusion model is introduced for the master equation of Markov jump processes in bounded domains. With minimal assumptions on the model parameters, the nonlocal steady and unsteady state master equations are shown to be well-posed in a weak sense. Then the nonlocal operator is shown to be the generator of finite-range nonsymmetric jump processes and, when certain conditions on the model parameters hold, the generators of finite and infinite activity Levy and Levy-type jump processes are shown to be special instances of the nonlocal operator.

• 出版日期2017-10