{"paper":{"title":"Multi-step Richardson-Romberg Extrapolation: Remarks on Variance Control and complexity","license":"","headline":"","cross_cats":["math.ST","stat.TH"],"primary_cat":"math.PR","authors_text":"Gilles Pag\\`es (PMA)","submitted_at":"2006-12-18T15:47:12Z","abstract_excerpt":"We propose a multi-step Richardson-Romberg extrapolation method for the computation of expectations $E f(X_{_T})$ of a diffusion $(X_t)_{t\\in [0,T]}$ when the weak time discretization error induced by the Euler scheme admits an expansion at an order $R\\ge 2$. The complexity of the estimator grows as $R^2$ (instead of $2^R$) and its variance is asymptotically controlled by considering some consistent Brownian increments in the underlying Euler schemes. Some Monte carlo simulations carried with path-dependent options (lookback, barriers) which support the conjecture that their weak time discreti"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0612523","kind":"arxiv","version":4},"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"}