{"paper":{"title":"Weak order for the discretization of the stochastic heat equation","license":"","headline":"","cross_cats":["cs.NA"],"primary_cat":"math.NA","authors_text":"Arnaud Debussche (IRMAR), Jacques Printems (LAMA)","submitted_at":"2007-10-29T15:06:29Z","abstract_excerpt":"In this paper we study the approximation of the distribution of $X_t$ Hilbert--valued stochastic process solution of a linear parabolic stochastic partial differential equation written in an abstract form as $$ dX_t+AX_t dt = Q^{1/2} d W_t, \\quad X_0=x \\in H, \\quad t\\in[0,T], $$ driven by a Gaussian space time noise whose covariance operator $Q$ is given. We assume that $A^{-\\alpha}$ is a finite trace operator for some $\\alpha>0$ and that $Q$ is bounded from $H$ into $D(A^\\beta)$ for some $\\beta\\geq 0$. It is not required to be nuclear or to commute with $A$. The discretization is achieved tha"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0710.5450","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/0710.5450/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}