{"paper":{"title":"Exponential forgetting of smoothing distributions for pairwise Markov models","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Joonas Sova, J\\\"uri Lember","submitted_at":"2021-03-09T15:05:30Z","abstract_excerpt":"We consider a bivariate Markov chain $Z=\\{Z_k\\}_{k \\geq 1}=\\{(X_k,Y_k)\\}_{k \\geq 1}$ taking values on product space ${\\cal Z}={\\cal X} \\times{ \\cal Y}$, where ${\\cal X}$ is possibly uncountable space and ${\\cal Y}=\\{1,\\ldots, |{\\cal Y}|\\}$ is a finite state-space. The purpose of the paper is to find sufficient conditions that guarantee the exponential convergence of smoothing, filtering and predictive probabilities: $$\\sup_{n\\geq t}\\|P(Y_{t:\\infty}\\in \\cdot|X_{l:n})-P(Y_{t:\\infty}\\in \\cdot|X_{s:n}) \\|_{\\rm TV} \\leq K_s \\alpha^{t}, \\quad \\mbox{a.s.}$$ Here $t\\geq s\\geq l\\geq 1$, $K_s$ is $\\sigm"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2103.05474","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2103.05474/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}