{"paper":{"title":"Sharp regularity near an absorbing boundary for solutions to second order SPDEs in a half-line with constant coefficients","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Sean Ledger","submitted_at":"2013-03-27T16:51:48Z","abstract_excerpt":"We prove that the weak version of the SPDE problem \\begin{align*} dV_{t}(x) & = [-\\mu V_{t}'(x) + \\frac{1}{2} (\\sigma_{M}^{2} + \\sigma_{I}^{2})V_{t}\"(x)]dt - \\sigma_{M} V_{t}'(x)dW^{M}_{t}, \\quad x > 0, \\\\ V_{t}(0) &= 0 \\end{align*} with a specified bounded initial density, $V_{0}$, and $W$ a standard Brownian motion, has a unique solution in the class of finite-measure valued processes. The solution has a smooth density process which has a probabilistic representation and shows degeneracy near the absorbing boundary. In the language of weighted Sobolev spaces, we describe the precise order of"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1303.6894","kind":"arxiv","version":2},"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"}