{"paper":{"title":"Computation of sensitivities for the invariant measure of a parameter dependent diffusion","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Benjamin Jourdain (CERMICS, MATHERIALS), MATHRISK), Rapha\\\"el Roux (LPMA), Roland Assaraf (LCT), Tony Leli\\`evre (CERMICS","submitted_at":"2015-09-04T06:23:10Z","abstract_excerpt":"We consider the solution to a stochastic differential equation with a drift function which depends smoothly on some real parameter $\\lambda$, and admitting a unique invariant measure for any value of $\\lambda$ around $\\lambda$ = 0. Our aim is to compute the derivative with respect to $\\lambda$ of averages with respect to the invariant measure, at $\\lambda$ = 0. We analyze a numerical method which consists in simulating the process at $\\lambda$ = 0 together with its derivative with respect to $\\lambda$ on long time horizon. We give sufficient conditions implying uniform-in-time square integrabi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1509.01348","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"}