{"paper":{"title":"Stable L\\'evy motion with values in the Skorokhod space: construction and approximation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Becem Saidani, Raluca M. Balan","submitted_at":"2018-09-06T17:25:34Z","abstract_excerpt":"In this article, we introduce an infinite-dimensional analogue of the $\\alpha$-stable L\\'evy motion, defined as a L\\'evy process $Z=\\{Z(t)\\}_{t \\geq 0}$ with values in the space $\\mathbb{D}$ of c\\`adl\\`ag functions on $[0,1]$, equipped with Skorokhod's $J_1$ topology. For each $t \\geq 0$, $Z(t)$ is an $\\alpha$-stable process with sample paths in $\\mathbb{D}$, denoted by $\\{Z(t,s)\\}_{s\\in [0,1]}$. Intuitively, $Z(t,s)$ gives the value of the process $Z$ at time $t$ and location $s$ in space. This process is closely related to the concept of regular variation for random elements in $\\mathbb{D}$ "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1809.02103","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"}