{"paper":{"title":"A discontinuous Galerkin method for approximating the stationary distribution of stochastic fluid-fluid processes","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Giang T. Nguyen, Malgorzata M. O'Reilly, Nigel Bean, Vikram Sunkara","submitted_at":"2019-01-30T01:43:59Z","abstract_excerpt":"Introduced by Bean and O'Reilly (2014), a stochastic fluid-fluid process is a Markov processes $\\{X_t, Y_t, \\varphi_t\\}_{t \\geq 0}$, where the first fluid $X_t$ is driven by the Markov chain $\\varphi_t$, and the second fluid $Y_t$ is driven by $\\varphi_t$ as well as by $X_t$. That paper derived a closed-form expression for the joint stationary distribution, given in terms of operators acting on measures, which does not lend itself easily to numerical computations.\n  Here, we construct a discontinuous Galerkin method for approximating this stationary distribution, and illustrate the methodology"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1901.10635","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"}