{"paper":{"title":"Concave majorant of stochastic processes and Burgers turbulence","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Raphael Lachieze-Rey","submitted_at":"2009-09-06T15:40:42Z","abstract_excerpt":"The asymptotic solution of the inviscid Burgers equations with initial potential $\\psi$ is closely related to the convex hull of the graph of $\\psi$.\n  In this paper, we study this convex hull, and more precisely its extremal points, if $\\psi$ is a stochastic process. The times where those extremal points are reached, called extremal times, form a negligible set for L\\'evy processes, their integrated processes, and It\\^o processes. We examine more closely the case of a L\\'evy process with bounded variation. Its extremal points are almost surely countable, with accumulation only around the extr"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0909.1088","kind":"arxiv","version":3},"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"}