{"paper":{"title":"Likelihood Ratio Gradient Estimation for Steady-State Parameters","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Mariana Olvera-Cravioto, Peter W. Glynn","submitted_at":"2017-07-09T23:48:23Z","abstract_excerpt":"We consider a discrete-time Markov chain $\\boldsymbol{\\Phi}$ on a general state-space ${\\sf X}$, whose transition probabilities are parameterized by a real-valued vector $\\boldsymbol{\\theta}$. Under the assumption that $\\boldsymbol{\\Phi}$ is geometrically ergodic with corresponding stationary distribution $\\pi(\\boldsymbol{\\theta})$, we are interested in estimating the gradient $\\nabla \\alpha(\\boldsymbol{\\theta})$ of the steady-state expectation $$\\alpha(\\boldsymbol{\\theta}) = \\pi( \\boldsymbol{\\theta}) f.$$\n  To this end, we first give sufficient conditions for the differentiability of $\\alpha("},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1707.02659","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"}