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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"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1605.02020","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2016-05-06T18:17:04Z","cross_cats_sorted":[],"title_canon_sha256":"ccb650bc736e41981c39bc47e2aa8deb341968dc3f67039db4659dbd4588560a","abstract_canon_sha256":"ee2f7af9d9a18968aa8cd2e11aa21ae377760a43f36f76b3b5d5937093b5ea3b"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:15:30.617998Z","signature_b64":"FwzQdbWnQcSqiEupR1p4AC6bAcVOxDcOH+rL5K0LoEkm5dtjdlU/DK3uM7rv/rS7CuKKYzJ6onMoj7fFp0xLCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7932554cf0b2a363246f809ac622afc85f8da28a90068a36fb49417d527f7c4c","last_reissued_at":"2026-05-18T01:15:30.617287Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:15:30.617287Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"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. 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