{"paper":{"title":"Existence and uniqueness for backward stochastic differential equations driven by a random measure","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Elena Bandini","submitted_at":"2015-06-07T10:33:10Z","abstract_excerpt":"We study the following backward stochastic differential equation on finite time horizon driven by an integer-valued random measure $\\mu$ on $\\mathbb R_+\\times E$, where $E$ is a Lusin space, with compensator $\\nu(dt,dx)=dA_t\\,\\phi_t(dx)$: \\[ Y_t = \\xi + \\int_{(t,T]} f(s,Y_{s-},Z_s(\\cdot))\\, d A_s - \\int_{(t,T]} \\int_E Z_s(x) \\, (\\mu-\\nu)(ds,dx),\\qquad 0\\leq t\\leq T. \\] The generator $f$ satisfies, as usual, a uniform Lipschitz condition with respect to its last two arguments. In the literature, the existence and uniqueness for the above equation in the present general setting has only been est"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1506.02249","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"}