{"paper":{"title":"Asymptotics for Exit Problem and Principal Eigenvalue for a Class of Non-Local Elliptic Operators Related to Diffusion Processes with Random Jumps and Vanishing Diffusion","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP"],"primary_cat":"math.PR","authors_text":"Ross G. Pinsky","submitted_at":"2011-05-18T12:57:18Z","abstract_excerpt":"Let $D\\subset R^d$ be a bounded domain and denote by $\\mathcal P(D)$ the space of probability measures on $D$. Let \\begin{equation*} L=\\frac12\\nabla\\cdot a\\nabla +b\\nabla \\end{equation*} be a second order elliptic operator. Let $\\mu\\in\\mathcal P(D)$ and $\\delta>0$.\n  Consider a Markov process $X(t)$ in $D$ which performs diffusion in $D$ generated by the operator $\\delta L$ and is stopped at the boundary, and which while running, jumps instantaneously, according to an exponential clock with spatially dependent intensity $V>0$, to a new point, according to the distribution $\\mu$. The Markov pro"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1105.3614","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}