{"paper":{"title":"Markov processes with jump kernels decaying at the boundary","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP"],"primary_cat":"math.PR","authors_text":"Panki Kim, Renming Song, Soobin Cho, Zoran Vondra\\v{c}ek","submitted_at":"2024-03-01T12:07:32Z","abstract_excerpt":"The goal of this work is to develop a general theory for non-local singular operators of the type $$\n  L^{\\mathcal{B}}_{\\alpha}f(x)=\\lim_{\\epsilon\\to 0} \\int_{D,\\, |y-x|>\\epsilon}\\big(f(y)-f(x)\\big) \\mathcal{B}(x,y)|x-y|^{-d-\\alpha}\\,dy, $$ and $$ L f(x)=L^{\\mathcal{B}}_{\\alpha}f(x) - \\kappa(x) f(x), $$ in case $D$ is a $C^{1,1}$ open set in $\\mathbb{R}^d$, $d\\ge 2$. The function $\\mathcal{B}(x,y)$ above may vanish at the boundary of $D$, and the killing potential $\\kappa$ may be subcritical or critical.\n  From a probabilistic point of view we study the reflected process on the closure $\\overl"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2403.00480","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2403.00480/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}