{"paper":{"title":"Branching diffusion representation for nonlinear Cauchyproblems and Monte Carlo approximation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.AP","math.MP","math.NA"],"primary_cat":"math.PR","authors_text":"2), (2) CMAP), Nizar Touzi (2) ((1) SOCIETE GENERALE, Pierre Henry-Labordere (1","submitted_at":"2018-01-26T13:08:23Z","abstract_excerpt":"We provide a probabilistic representations of the solution of some semilinear hyperbolicand high-order PDEs based on branching diffusions. These representations pave theway for a Monte-Carlo approximation of the solution, thus bypassing the curse ofdimensionality. We illustrate the numerical implications in the context of some popularPDEs in physics such as nonlinear Klein-Gordon equation, a simplied scalar versionof the Yang-Mills equation, a fourth-order nonlinear beam equation and the Gross-Pitaevskii PDEas an example of nonlinear Schrodinger equations."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1801.08794","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"}