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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 L\u00e9vy and L\u00e9vy-type jump processes are shown to be special instances of the nonlocal operator.<\/jats:p>","DOI":"10.1515\/cmam-2017-0029","type":"journal-article","created":{"date-parts":[[2017,8,31]],"date-time":"2017-08-31T10:00:44Z","timestamp":1504173644000},"page":"707-722","source":"Crossref","is-referenced-by-count":44,"title":["Nonlocal Convection-Diffusion Problems on Bounded Domains and Finite-Range Jump Processes"],"prefix":"10.1515","volume":"17","author":[{"given":"Marta","family":"D\u2019Elia","sequence":"first","affiliation":[{"name":"Center for Computing Research , Sandia National Laboratories , Albuquerque , NM 87123 , USA"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-1067-8937","authenticated-orcid":false,"given":"Qiang","family":"Du","sequence":"additional","affiliation":[{"name":"Department of Applied Physics and Applied Mathematics , Fu Foundation School of Engineering and Applied Sciences , Columbia University , New York , NY 10027 , USA"}]},{"given":"Max","family":"Gunzburger","sequence":"additional","affiliation":[{"name":"Department of Scientific Computing , Florida State University , Tallahassee , FL 32306-4120 , USA"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-2579-1374","authenticated-orcid":false,"given":"Richard","family":"Lehoucq","sequence":"additional","affiliation":[{"name":"Center for Computing Research , Sandia National Laboratories , Albuquerque , NM 87123 , USA"}]}],"member":"374","published-online":{"date-parts":[[2017,8,31]]},"reference":[{"key":"2023033116270854848_j_cmam-2017-0029_ref_001_w2aab3b7b5b1b6b1ab1b4b1Aa","doi-asserted-by":"crossref","unstructured":"B.  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