{"paper":{"title":"Entropy and Grand Lebesgue Spaces approach for Prokhorov-Skorokhod continuity of random processes, with tail estimates","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"E. Ostrovsky, L. Sirota","submitted_at":"2015-12-07T04:41:04Z","abstract_excerpt":"We present in this paper a new sufficient condition for the so-called Prokhorov-Skorokhod continuity of random processes. Our conditions will be formulated in the terms of metric entropy generated by three-dimensional distribution of the considered random process (r.p.) in the parametric set, have a convenient and closed form, and generalize some previous results.\n  We study also the conditions for weak compactness of the sequence of random processes in this space and as a consequence the Central Limit Theorem.\n  Our consideration based on the theory of Prokhorov-Skorokhod spaces of random pro"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1512.01909","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"}