{"paper":{"title":"Feedback control: two-sided Markov-modulated Brownian motion with instantaneous change of phase at boundaries","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Giang T. Nguyen, Guy Latouche","submitted_at":"2016-03-07T05:51:07Z","abstract_excerpt":"We consider a Markov-modulated Brownian motion $\\{Y(t), \\rho(t)\\}$ with two boundaries at $0$ and $b > 0$, and allow for the controlling Markov chain $\\{\\rho(t)\\}$ to instantaneously undergo a change of phase upon hitting either of the two boundaries at semi-regenerative epochs defined to be the first time the process reaches a boundary since it last hits the other boundary. We call this process a flexible Markov-modulated Brownian motion.\n  Using the recently-established links between stochastic fluid models and Markov-modulated Brownian motions, we determine important characteristics of firs"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1603.01945","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"}