{"paper":{"title":"A note on $\\alpha$-IDT processes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Antoine Hakassou, Youssef Ouknine","submitted_at":"2012-03-05T11:56:09Z","abstract_excerpt":"In this note, we introduce the notion of $\\alpha$-IDT processes which is obtained from a slight and fundamental modification of the IDT property. Several examples of $\\alpha$-IDT processes are given and Gaussian processes which are $\\alpha$-IDT are characterized. A kind example of this Gaussian $\\alpha$-IDT is the standard fractional Brownian motion. Also, we invest some links between the $\\alpha$-IDT property, with selfdecomposability, temporal selfdecomposability, stability and self similarity."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1203.0874","kind":"arxiv","version":3},"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"}