{"paper":{"title":"Processes iterated ad libitum","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Jean-Fran\\c{c}ois Marckert, J\\'er\\^ome Casse","submitted_at":"2015-04-24T09:14:40Z","abstract_excerpt":"Consider the $n$th iterated Brownian motion $I^{(n)}=B_n \\circ\\cdots \\circ B_1$. Curien and Konstantopoulos proved that for any distinct numbers $t_i\\neq 0$, $(I^{(n)}(t_1),\\dots,I^{(n)}(t_k))$ converges in distribution to a limit $I[k]$ independent of the $t_i$'s, exchangeable, and gave some elements on the limit occupation measure of $I^{(n)}$. Here, we prove under some conditions, finite dimensional distributions of $n$th iterated two-sided stable processes converge, and the same holds the reflected Brownian motions. We give a description of the law of $I[k]$, of the finite dimensional dist"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1504.06433","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"}