{"paper":{"title":"Quadratic covariations for the solution to a stochastic heat equation","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Litan Yan, Xianye Yu, Xichao Sun","submitted_at":"2016-02-29T02:13:53Z","abstract_excerpt":"Let $u(t,x)$ be the solution to a stochastic heat equation $$ \\frac{\\partial}{\\partial t}u=\\frac12\\frac{\\partial^2}{\\partial x^2}u+\\frac{\\partial^2}{\\partial t\\partial x}X(t,x),\\quad t\\geq 0, x\\in {\\mathbb R} $$ with initial condition $u(0,x)\\equiv 0$, where $X$ is a time-space white noise. This paper is an attempt to study stochastic analysis questions of the solution $u(t,x)$. In fact, the solution is a Gaussian process such that the process $t\\mapsto u(t,\\cdot)$ is a bi-fractional Brownian motion seemed a fractional Brownian motion with Hurst index $H=\\frac14$ for every real number $x$. How"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1602.08796","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"}