{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,7]],"date-time":"2026-04-07T02:06:38Z","timestamp":1775527598925,"version":"3.50.1"},"reference-count":24,"publisher":"Cambridge University Press (CUP)","issue":"1","license":[{"start":{"date-parts":[[2025,8,19]],"date-time":"2025-08-19T00:00:00Z","timestamp":1755561600000},"content-version":"unspecified","delay-in-days":0,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":["cambridge.org"],"crossmark-restriction":true},"short-container-title":["J. Appl. Probab."],"published-print":{"date-parts":[[2026,3]]},"abstract":"<jats:title>Abstract<\/jats:title>\n                  <jats:p>\n                    Let\n                    <jats:inline-formula>\n                      <jats:alternatives>\n                        <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"png\" xlink:href=\"S0021900225100259_inline1.png\"\/>\n                        <jats:tex-math>$\\pi$<\/jats:tex-math>\n                      <\/jats:alternatives>\n                    <\/jats:inline-formula>\n                    be a probability distribution in\n                    <jats:inline-formula>\n                      <jats:alternatives>\n                        <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"png\" xlink:href=\"S0021900225100259_inline2.png\"\/>\n                        <jats:tex-math>$\\mathbb{R}^d$<\/jats:tex-math>\n                      <\/jats:alternatives>\n                    <\/jats:inline-formula>\n                    and\n                    <jats:italic>f<\/jats:italic>\n                    a test function, and consider the problem of variance reduction in estimating\n                    <jats:inline-formula>\n                      <jats:alternatives>\n                        <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"png\" xlink:href=\"S0021900225100259_inline3.png\"\/>\n                        <jats:tex-math>$\\mathbb{E}_\\pi(f)$<\/jats:tex-math>\n                      <\/jats:alternatives>\n                    <\/jats:inline-formula>\n                    . We first construct a sequence of estimators for\n                    <jats:inline-formula>\n                      <jats:alternatives>\n                        <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"png\" xlink:href=\"S0021900225100259_inline4.png\"\/>\n                        <jats:tex-math>$\\mathbb{E}_\\pi (f)$<\/jats:tex-math>\n                      <\/jats:alternatives>\n                    <\/jats:inline-formula>\n                    , say\n                    <jats:inline-formula>\n                      <jats:alternatives>\n                        <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"png\" xlink:href=\"S0021900225100259_inline5.png\"\/>\n                        <jats:tex-math>$({1}\/{k})\\sum_{i=0}^{k-1} g_n(X_i)$<\/jats:tex-math>\n                      <\/jats:alternatives>\n                    <\/jats:inline-formula>\n                    , where the\n                    <jats:inline-formula>\n                      <jats:alternatives>\n                        <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"png\" xlink:href=\"S0021900225100259_inline6.png\"\/>\n                        <jats:tex-math>$X_i$<\/jats:tex-math>\n                      <\/jats:alternatives>\n                    <\/jats:inline-formula>\n                    are samples from\n                    <jats:inline-formula>\n                      <jats:alternatives>\n                        <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"png\" xlink:href=\"S0021900225100259_inline7.png\"\/>\n                        <jats:tex-math>$\\pi$<\/jats:tex-math>\n                      <\/jats:alternatives>\n                    <\/jats:inline-formula>\n                    generated by the Metropolized Hamiltonian Monte Carlo algorithm and\n                    <jats:inline-formula>\n                      <jats:alternatives>\n                        <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"png\" xlink:href=\"S0021900225100259_inline8.png\"\/>\n                        <jats:tex-math>$g_n$<\/jats:tex-math>\n                      <\/jats:alternatives>\n                    <\/jats:inline-formula>\n                    is the approximate solution of the Poisson equation through the weak approximate scheme recently invented by Mijatovi\u0107 and Vogrinc (2018). Then we prove under some regularity assumptions that the estimation error variance\n                    <jats:inline-formula>\n                      <jats:alternatives>\n                        <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"png\" xlink:href=\"S0021900225100259_inline9.png\"\/>\n                        <jats:tex-math>$\\sigma_\\pi^2(g_n)$<\/jats:tex-math>\n                      <\/jats:alternatives>\n                    <\/jats:inline-formula>\n                    can be as arbitrarily small as the approximation order parameter\n                    <jats:inline-formula>\n                      <jats:alternatives>\n                        <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"png\" xlink:href=\"S0021900225100259_inline10.png\"\/>\n                        <jats:tex-math>$n\\rightarrow\\infty$<\/jats:tex-math>\n                      <\/jats:alternatives>\n                    <\/jats:inline-formula>\n                    . To illustrate, we confirm that the assumptions are satisfied by two typical concrete models, a Bayesian linear inverse problem and a two-component mixture of Gaussian distributions.\n                  <\/jats:p>","DOI":"10.1017\/jpr.2025.10025","type":"journal-article","created":{"date-parts":[[2025,8,19]],"date-time":"2025-08-19T06:41:01Z","timestamp":1755585661000},"page":"177-203","update-policy":"https:\/\/doi.org\/10.1017\/policypage","source":"Crossref","is-referenced-by-count":0,"title":["On the variance reduction of Hamiltonian Monte Carlo via an approximation scheme"],"prefix":"10.1017","volume":"63","author":[{"given":"Zhonggen","family":"Su","sequence":"first","affiliation":[{"name":"Zhejiang University"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Zeyu","family":"Yao","sequence":"additional","affiliation":[{"name":"Zhejiang University"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"56","published-online":{"date-parts":[[2025,8,19]]},"reference":[{"key":"S0021900225100259_ref2","unstructured":"[2] Betancourt, M. (2018). A conceptual introduction to Hamiltonian Monte Carlo. Preprint, arXiv:1701.02434."},{"key":"S0021900225100259_ref5","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-319-97704-1"},{"key":"S0021900225100259_ref19","doi-asserted-by":"publisher","DOI":"10.1214\/aoap\/1034625254"},{"key":"S0021900225100259_ref18","doi-asserted-by":"publisher","DOI":"10.1214\/11-AAP828"},{"key":"S0021900225100259_ref15","doi-asserted-by":"publisher","DOI":"10.1073\/pnas.1820003116"},{"key":"S0021900225100259_ref9","doi-asserted-by":"publisher","DOI":"10.1214\/19-AOS1941"},{"key":"S0021900225100259_ref8","doi-asserted-by":"publisher","DOI":"10.1007\/s11222-014-9511-z"},{"key":"S0021900225100259_ref21","doi-asserted-by":"publisher","DOI":"10.1214\/154957804100000024"},{"key":"S0021900225100259_ref1","doi-asserted-by":"publisher","DOI":"10.1214\/105051604000000710"},{"key":"S0021900225100259_ref11","doi-asserted-by":"publisher","DOI":"10.1007\/s10959-023-01240-1"},{"key":"S0021900225100259_ref13","unstructured":"[13] Jin, R. and Tan, X. (2020). Central limit theorems for Markov chains based on their convergence rates in Wasserstein distance. Preprint, arXiv:2002.09427."},{"key":"S0021900225100259_ref4","doi-asserted-by":"publisher","DOI":"10.1201\/b10905"},{"key":"S0021900225100259_ref3","doi-asserted-by":"publisher","DOI":"10.1017\/S0962492917000101"},{"key":"S0021900225100259_ref22","doi-asserted-by":"publisher","DOI":"10.2307\/3318418"},{"key":"S0021900225100259_ref24","doi-asserted-by":"publisher","DOI":"10.1016\/j.spl.2014.04.002"},{"key":"S0021900225100259_ref7","volume-title":"Multidimensional Real Analysis I: Differentiation","author":"Duistermaat","year":"2004"},{"key":"S0021900225100259_ref6","doi-asserted-by":"publisher","DOI":"10.1016\/0370-2693(87)91197-X"},{"key":"S0021900225100259_ref12","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-642-39363-1"},{"key":"S0021900225100259_ref16","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9780511626630"},{"key":"S0021900225100259_ref14","doi-asserted-by":"crossref","unstructured":"[14] Kamatani, K. and Song, X. (2021). Haar\u2013Weave\u2013Metropolis kernel. 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Preprint, arXiv:2108.12107."},{"key":"S0021900225100259_ref10","doi-asserted-by":"publisher","DOI":"10.1214\/19-EJP287"},{"key":"S0021900225100259_ref20","doi-asserted-by":"publisher","DOI":"10.1111\/1467-9868.00123"},{"key":"S0021900225100259_ref17","doi-asserted-by":"publisher","DOI":"10.3150\/17-BEJ932"}],"container-title":["Journal of Applied Probability"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0021900225100259","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,4,7]],"date-time":"2026-04-07T01:25:39Z","timestamp":1775525139000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0021900225100259\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,8,19]]},"references-count":24,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2026,3]]}},"alternative-id":["S0021900225100259"],"URL":"https:\/\/doi.org\/10.1017\/jpr.2025.10025","relation":{},"ISSN":["0021-9002","1475-6072"],"issn-type":[{"value":"0021-9002","type":"print"},{"value":"1475-6072","type":"electronic"}],"subject":[],"published":{"date-parts":[[2025,8,19]]},"assertion":[{"value":"\u00a9 The Author(s), 2025. Published by Cambridge University Press on behalf of Applied Probability Trust","name":"copyright","label":"Copyright","group":{"name":"copyright_and_licensing","label":"Copyright and Licensing"}}]}}