skip to main content


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

In this paper, 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. Finally, 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 Lévy and Lévy-type jump processes are shown to be special instances of the nonlocal operator.
 [1] ; ORCiD logo [2] ;  [3] ; ORCiD logo [1]
  1. Sandia National Lab. (SNL-NM), Albuquerque, NM (United States). Center for Computing Research
  2. Columbia Univ., New York, NY (United States). Dept. of Applied Physics and Applied Mathematics. Fu Foundation School of Engineering and Applied Sciences
  3. Florida State Univ., Tallahassee, FL (United States). Dept. of Scientific Computing
Publication Date:
Report Number(s):
Journal ID: ISSN 1609-4840; 667563
Grant/Contract Number:
NA0003525; SC0009324; FA9550-14-1-0073; W911NF-15-1-0562; HR0011619523; 1868-A017-15; DMS-1315259
Accepted Manuscript
Journal Name:
Computational Methods in Applied Mathematics
Additional Journal Information:
Journal Volume: 17; Journal Issue: 4; Journal ID: ISSN 1609-4840
de Gruyter
Research Org:
Sandia National Lab. (SNL-NM), Albuquerque, NM (United States); Florida State Univ., Tallahassee, FL (United States); Columbia Univ., New York, NY (United States)
Sponsoring Org:
USDOE National Nuclear Security Administration (NNSA); USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR) (SC-21); US Air Force Office of Scientific Research (AFOSR); US Army Research Office (ARO); Defense Advanced Research Projects Agency (DARPA) (United States); National Science Foundation (NSF)
Country of Publication:
United States
97 MATHEMATICS AND COMPUTING; nonlocal diffusion; nonlocal operators; nonlocal vector calculus; variational forms; master equation; Markov processes; Lévy processes
OSTI Identifier: