{"paper":{"title":"Stability of multidimensional skip-free Markov modulated reflecting random walks: Revisit to Malyshev and Menshikov's results and application to queueing networks","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Toshihisa Ozawa","submitted_at":"2012-08-15T06:46:12Z","abstract_excerpt":"Let $\\{\\boldsymbol{X}_n\\}$ be a discrete-time $d$-dimensional process on $\\mathbb{Z}_+^d$ with a supplemental (background) process $\\{J_n\\}$ on a finite set and assume the joint process $\\{\\boldsymbol{Y}_n\\}=\\{(\\boldsymbol{X}_n,J_n)\\}$ to be Markovian. Then, the process $\\{\\boldsymbol{X}_n\\}$ can be regarded as a kind of reflecting random walk (RRW for short) in which the transition probabilities of the RRW are modulated according to the state of the background process $\\{J_n\\}$; we assume this modulation is space-homogeneous inside $\\mathbb{Z}_+^d$ and on each boundary face of $\\mathbb{Z}_+^d"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1208.3043","kind":"arxiv","version":4},"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"}