{"paper":{"title":"Embedding of Walsh Brownian Motion","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.OC"],"primary_cat":"math.PR","authors_text":"Erhan Bayraktar, Xin Zhang","submitted_at":"2019-05-30T01:19:56Z","abstract_excerpt":"Let $(Z,\\kappa)$ be a Walsh Brownian motion with spinning measure $\\kappa$. Suppose $\\mu$ is a probability measure on $\\mathbb{R}^n$. We characterize all the $\\kappa$ such that $\\mu$ is a stopping distribution of $(Z,\\kappa)$. If we further restrict the solution to be integrable, we show that there would be only one choice of $\\kappa$. We also generalize Vallois' embedding, and prove that it minimizes the expectation $\\mathbb{E}[\\Psi(L^Z_{\\tau})]$ among all the admissible solutions $\\tau$, where $\\Psi$ is a strictly convex function and $(L_t^Z)_{t \\geq 0}$ is the local time of the Walsh Browni"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1905.12811","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"}