{"paper":{"title":"A Dirichlet Process Characterization of RBM in a Wedge","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Bert Zwart, Josh Reed, Peter Lakner","submitted_at":"2016-05-06T18:17:04Z","abstract_excerpt":"Reflected Brownian motion (RBM) in a wedge is a 2-dimensional stochastic process Z whose state space in R^2 is given in polar coordinates by S={(r,theta): r >= 0, 0 <= theta <= xi} for some 0 < xi < 2 pi. Let alpha= (theta_1+theta_2)/xi, where -pi/2 < theta_1,theta_2 < pi/2 are the directions of reflection of Z off each of the two edges of the wedge as measured from the corresponding inward facing normal. We prove that in the case of 1 < alpha < 2, RBM in a wedge is a Dirichlet process. Specifically, its unique Doob-Meyer type decomposition is given by Z=X+Y, where X is a two-dimensional Brown"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1605.02020","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"}