{"paper":{"title":"p-variation of strong Markov processes","license":"","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Martynas Manstavicius","submitted_at":"2004-10-05T17:10:12Z","abstract_excerpt":"Let \\xi_t, t\\in[0,T], be a strong Markov process with values in a complete separable metric space (X,\\rho) and with transition probability function\n P_{s,t}(x,dy), 0\\le s\\le t\\le T, x\\in X. For any h\\in[0,T] and a>0, consider the function \\alpha(h,a)=sup\\bigl{P_{s,t}\\bigl(x,{y:\\rho(x,y)\\ge a}\\bigr):x\\in X,0\\le s\\le t\\le (s+h)\\wedge T\\bigr}. It is shown that a certain growth condition on \\alpha(h,a), as a\\downarrow0 and h stays fixed, implies the almost sure boundedness of the p-variation of \\xi_t, where p depends on the rate of growth."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0410106","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"}