{"paper":{"title":"On the spatial dynamics of the solution to the stochastic heat equation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP"],"primary_cat":"math.PR","authors_text":"James Bichard, Sigurd Assing","submitted_at":"2013-05-14T23:51:23Z","abstract_excerpt":"We consider the solution of $\\partial_t u=\\partial_x^2 u+\\partial_x\\partial_t B,\\,(x,t)\\in R\\times(0,\\infty)$, subject to $u(x,0)=0,\\,x\\in R$, where $B$ is a Brownian sheet. We show that $u$ also satisfies $\\partial_x^2 u +[\\,(-\\partial_t^2)^{1/2}+\\sqrt{2}\\partial_x(-\\partial_t^2)^{1/4}\\,]\\,u^a= \\partial_x\\partial_t{\\tilde B}$ in $R\\times(0,\\infty)$ where $u^a$ stands for the extension of $u(x,t)$ to $(x,t)\\in R^2$ which is antisymmetric in $t$ and $\\tilde{B}$ is another Brownian sheet. The new SPDE allows us to prove the strong Markov property of the pair $(u,\\partial_x u)$ when seen as a pro"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1305.3325","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"}