{"paper":{"title":"Approximation in law of locally $\\alpha$-stable L\\'evy-type processes by non-linear regressions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Alexei Kulik","submitted_at":"2018-08-21T06:33:34Z","abstract_excerpt":"We study a real-valued L\\'evy-type process $X$, which is locally $\\alpha$-stable in the sense that its jump kernel is a combination of a `principal' (state dependent) $\\alpha$-stable part with a `residual' lower order part. We show that under mild conditions on the local characteristics of a process (the jump kernel and the velocity field) the process is uniquely defined, is Markov, and has the strong Feller property. We approximate $X$ in law by a non-linear regression $\\widetilde X^x_{t}=\\mathfrak{f}_t(x)+t^{1/\\alpha}U^{x}_t$ with a deterministic regressor term $\\mathfrak{f}_t(x)$ and $\\alph"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1808.06779","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"}