{"paper":{"title":"Analytic properties of Markov semigroup generated by Stochastic Differential Equations driven by L\\'evy processes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Erika Hausenblas, Pani W. Fernando, Paul Razafimandimby","submitted_at":"2014-12-03T19:41:44Z","abstract_excerpt":"We consider the stochastic differential equations of the form \\begin{equation*} \\begin{cases} dX^ x(t) = \\sigma(X(t-)) dL(t) \\\\ X^ x(0)=x,\\quad x\\in\\mathbb{R}^ d, \\end{cases} \\end{equation*} where $\\sigma:\\mathbb{R}^ d\\to \\mathbb{R}^ d$ is Lipschitz continuous and $L=\\{L(t):t\\ge 0\\}$ is a L\\'evy process. Under this condition on $\\sigma$ it is well known that the above problem has a unique solution $X$. Let $(\\mathcal{P}_{t})_{t\\ge0}$ be the Markovian semigroup associated to $X$ defined by $( \\mathcal{P}_t f) (x) := \\mathbb{E} [ f(X^ x(t))]$, $t\\ge 0$, $x\\in \\mathbb{R}^d$, $f\\in \\mathcal{B}_b(\\"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1412.1453","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"}