{"paper":{"title":"Space-time fractional equations and the related stable processes at random time","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Bruno Toaldo, Enzo Orsingher","submitted_at":"2012-07-13T15:44:40Z","abstract_excerpt":"In this paper we consider the general fractional equation \\sum_{j=1}^m \\lambda_j \\frac{\\partial^{\\nu_j}}{\\partial t^{\\nu_j}} w(x_1,..., x_n ; t) = -c^2 (-\\Delta)^\\beta w(x_1,..., x_n ; t), for \\nu_j \\in (0,1], \\beta \\in (0,1] with initial condition w(x_1,..., x_n ; 0)= \\prod_{j=1}^n \\delta (x_j). The solution of the Cauchy problem above coincides with the distribution of the n-dimensional process \\bm{S}_n^{2\\beta} \\mathcal{L} c^2 {L}^{\\nu_1,..., \\nu_m} (t) \\r, t>0, where \\bm{S}_n^{2\\beta} is an isotropic stable process independent from {L}^{\\nu_1,..., \\nu_m}(t) which is the inverse of {H}^{\\nu"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1207.3284","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"}