{"paper":{"title":"On the exact asymptotics of exit time from a cone of an isotropic $\\alpha$-self-similar Markov process with a skew-product structure","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Longmin Wang, Zbigniew Palmowski","submitted_at":"2016-10-02T21:55:00Z","abstract_excerpt":"In this paper we identify the asymptotic tail of the distribution of the exit time $\\tau_C$ from a cone $C$ of an isotropic $\\alpha$-self-similar Markov process $X_t$ with a skew-product structure, that is $X_t$ is a product of its radial process and independent time changed angular component $\\Theta_t$. Under some additional regularity assumptions, the angular process $\\Theta_t$ killed on exiting from the cone $C$ has the transition density that could be expressed in terms of a complete set of orthogonal eigenfunctions with corresponding eigenvalues of an appropriate generator. Using this fac"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1610.00358","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"}