Nonlocal Convection-Diffusion Problems on Bounded Domains and Finite-Range Jump Processes
Abstract
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 Lévy and Lévy-type jump processes are shown to be special instances of the nonlocal operator.
Document Details
- Document Type
- Pub Defense Publication
- Publication Date
- Aug 31, 2017
- Source ID
- 10.1515/cmam-2017-0029
Entities
People
- Marta D’Elia
- Max Gunzburger
- Qiang Du
- Richard B. Lehoucq
Organizations
- Air Force Office of Scientific Research
- Army Research Office
- Columbia University
- Defense Advanced Research Projects Agency
- Florida State University
- National Nuclear Security Administration
- National Science Foundation Division of Mathematical Sciences
- Oak Ridge National Laboratory
- Office of Advanced Scientific Computing Research
- Sandia National Laboratories