{"paper":{"title":"H\\\"older regularity and series representation of a class of stochastic volatility models","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Antoine Ayache, Qidi Peng","submitted_at":"2012-08-06T07:50:03Z","abstract_excerpt":"Let $\\Phi:\\R\\rightarrow\\R$ be an arbitrary continuously differentiable deterministic function such that $|\\Phi|+|\\Phi'|$ is bounded by a polynomial. In this article we consider the class of stochastic volatility models in which ${Z(t)}_{t\\in [0,1]}$, the logarithm of the price process, is of the form $Z(t)=\\int_{0}^t \\Phi(X(s)) dW(s)$, where ${X(s)}_{s\\in[0,1]}$ denotes an arbitrary centered Gaussian process whose trajectories are, with probability 1, H\\\"older continuous functions of an arbitrary order $\\alpha\\in (1/2,1]$, and where ${W(s)}_{s\\in[0,1]}$ is a standard Brownian motion independen"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1208.1100","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"}