{"paper":{"title":"Higher order PDE's and iterated Processes","license":"","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Erkan Nane","submitted_at":"2005-08-15T15:47:03Z","abstract_excerpt":"We introduce a class of stochastic processes based on symmetric $\\alpha$-stable processes.\n These are obtained by taking Markov processes and replacing the time parameter with the modulus of a symmetric $\\alpha$-stable process. We call them $\\alpha$-time processes. They generalize Brownian time processes studied in \\cite{allouba1, allouba2, allouba3}, and they introduce new interesting examples. We establish the connection of\n $\\alpha-$time processes to some higher order PDE's for $\\alpha$ rational. We also study the exit problem for $\\alpha$-time processes as they exit regular domains and con"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0508262","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"}