{"paper":{"title":"Optimizing the Drift in a Diffusive Search for a Random Stationary Target","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Ross G. Pinsky","submitted_at":"2018-03-28T08:40:38Z","abstract_excerpt":"Let $a\\in\\mathbb{R}$ denote an unknown stationary target with a known distribution $\\mu\\in\\mathcal{P(\\mathbb{R}})$, the space of probability measures on $\\mathbb{R}$. A diffusive searcher $X(\\cdot)$ sets out from the origin to locate the target. The time to locate the target is $T_a=\\inf\\{t\\ge0: X(t)=a\\}$. The searcher has a given constant diffusion rate $D>0$, but its drift $b$ can be set by the search designer from a natural admissible class $\\mathcal{D}_\\mu$ of drifts. Thus, the diffusive searcher is a Markov process generated by the operator $L=\\frac D2\\frac{d^2}{dx^2}+b(x)\\frac d{dx}$. % "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1803.10463","kind":"arxiv","version":3},"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"}