{"paper":{"title":"Equations of Mathematical Physics and Compositions of Brownian and Cauchy processes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP"],"primary_cat":"math.PR","authors_text":"Enzo Orsingher, Luisa Beghin, Lyudmyla Sakhno","submitted_at":"2010-08-05T08:51:53Z","abstract_excerpt":"We consider different types of processes obtained by composing Brownian motion $B(t)$, fractional Brownian motion $B_{H}(t)$ and Cauchy processes $% C(t)$ in different manners.\n  We study also multidimensional iterated processes in $\\mathbb{R}^{d},$ like, for example, $\\left( B_{1}(|C(t)|),...,B_{d}(|C(t)|)\\right) $ and $\\left( C_{1}(|C(t)|),...,C_{d}(|C(t)|)\\right) ,$ deriving the corresponding partial differential equations satisfied by their joint distribution.\n  We show that many important partial differential equations, like wave equation, equation of vibration of rods, higher-order heat "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1008.0928","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"}