{"paper":{"title":"Statistical estimation of jump rates for a specific class of Piecewise Deterministic Markov Processes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["stat.TH"],"primary_cat":"math.ST","authors_text":"Nathalie Krell (IRMAR)","submitted_at":"2014-06-11T09:51:33Z","abstract_excerpt":"We consider the class of   Piecewise Deterministic Markov Processes (PDMP), whose state space is $\\R\\_{+}^{*}$, that possess an increasing deterministic motion and that shrink deterministically when they jump. Well known examples for this class of processes are Transmission Control Protocol (TCP) window\nsize process   and the processes modeling the size of a \"marked\" {\\it Escherichia coli} cell. Having observed the PDMP until its $n$th jump, we construct a nonparametric estimator of the jump rate $\\lambda$. Our main result is that for  $D$ a compact subset of $\\R\\_{+}^{*}$, if  $\\lambda$  is i"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1406.2845","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"}