{"paper":{"title":"Exact asymptotic formulae of the stationary distribution of a discrete-time 2d-QBD process: an example and additional proofs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Masahiro Kobayashi, Toshihisa Ozawa","submitted_at":"2018-05-13T01:03:44Z","abstract_excerpt":"A discrete-time two-dimensional quasi-birth-and-death process (2d-QBD process), $\\{{\\boldsymbol{Y}}_n\\}=\\{(X_{1,n},X_{2,n},J_n)\\}$, is a two-dimensional skip-free random walk $\\{(X_{1,n},X_{2,n})\\}$ on $\\mathbb{Z}_+^2$ with a supplemental process $\\{J_n\\}$ on a finite set $S_0$. The supplemental process $\\{J_n\\}$ is called a phase process. The 2d-QBD process $\\{{\\boldsymbol{Y}}_n\\}$ is a Markov chain in which the transition probabilities of the two-dimensional process $\\{(X_{1,n},X_{2,n})\\}$ vary according to the state of the phase process $\\{J_n\\}$. This modulation is assumed to be space homo"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1805.04802","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"}