{"paper":{"title":"On the mixing structure of stationary increment and self-similar symmetric \\alpha-stable processes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Donatas Surgailis, Jan Rosinski, Stamatis Cambanis, V. Mandrekar","submitted_at":"2012-11-27T20:49:26Z","abstract_excerpt":"Mixed moving average processes appear in the ergodic decomposition of stationary symmetric \\alpha-stable (S\\alpha S) processes. They correspond to the dissipative part of \"deterministic\" flows generating S\\alpha S processes (Rosinski, 1995). Along these lines we study stationary increment and self-similar S\\alpha S processes. Since the classes of stationary increment and self-similar processes can be embedded into the class of stationary processes by the Masani and Lamperti transformations, respectively, we characterize these classes of S\\alpha S processes in terms of nonsingular flows and the"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1211.6419","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"}