{"paper":{"title":"Sample Path Properties of Volterra Processes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Eyal Neuman, Leonid Mytnik","submitted_at":"2011-01-25T22:45:39Z","abstract_excerpt":"We consider the regularity of sample paths of Volterra processes. These processes are defined as stochastic integrals $$ M(t)=\\int_{0}^{t}F(t,r)dX(r), \\ \\ t \\in \\mathds{R}_{+}, $$ where $X$ is a semimartingale and $F$ is a deterministic real-valued function. We derive the information on the modulus of continuity for these processes under regularity assumptions on the function $F$ and show that $M(t)$ has \"worst\" regularity properties at times of jumps of $X(t)$. We apply our results to obtain the optimal H\\\"older exponent for fractional L\\'{e}vy processes."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1101.4969","kind":"arxiv","version":2},"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"}