{"paper":{"title":"On the Finite Dimensional Joint Characteristic Function of L\\'{e}vy's Stochastic Area Processes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Xi Geng, Zhongmin Qian","submitted_at":"2012-06-06T14:17:46Z","abstract_excerpt":"The goal of this paper is to derive a formula for the finite dimensional joint characteristic function (the Fourier transform of the finite dimensional distribution) of the coupled process ${(W_{t},L_{t}^{A}):t\\in \\lbrack 0,\\infty)}$, where $\\{W_{t}:t\\in \\lbrack 0,\\infty)}$ is a $d$-dimensional Brownian motion and $\\{L_{t}^{A}:t\\in \\lbrack 0,\\infty)}$ is the generalized $d$-dimensional L$\\acute{e}$vy's stochastic area process associated to a $d\\times d$ matrix $A.$ Here $A$ need not be skew-symmetric, and in our computation we allow $A$ to vary. The problem finally reduces to the solution of a"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1206.1241","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"}