{"paper":{"title":"Well-balanced Levy Driven Ornstein-Uhlenbeck Processes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Alexander Schnurr, Jeannette H.C. Woerner","submitted_at":"2010-12-03T10:24:32Z","abstract_excerpt":"In this paper we introduce the well-balanced L\\'{e}vy driven Ornstein-Uhlenbeck process as a moving average process of the form $X_t=\\int \\exp(-\\lambda |t-u|)dL_u$. In contrast to L\\'{e}vy driven Ornstein-Uhlenbeck processes the well-balanced form possesses continuous sample paths and an autocorrelation function which is decreasing not purely exponential but of the order $\\lambda |u|\\exp(-\\lambda |u|)$. Furthermore, depending on the size of $\\lambda$ it allows both for positive and negative correlation of increments. We indicate how the well-balanced Ornstein-Uhlenbeck process might be used as"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1012.0691","kind":"arxiv","version":2},"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"}