{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2023,10,5]],"date-time":"2023-10-05T01:06:31Z","timestamp":1696467991106},"reference-count":18,"publisher":"Cambridge University Press (CUP)","issue":"04","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["J. Appl. Probab."],"published-print":{"date-parts":[[2015,12]]},"abstract":"<jats:p>Let<jats:italic>f<\/jats:italic>be an integrable function on an infinite measure space (S,<jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"gif\" xlink:href=\"S0021900200113129_inline1\" xlink:type=\"simple\" \/>, \u03c0). We show that if a<jats:italic>regenerative sequence<\/jats:italic>{<jats:italic>X<jats:sub>n<\/jats:sub><\/jats:italic>}<jats:sub><jats:italic>n<\/jats:italic>\u22650<\/jats:sub>with canonical measure<jats:italic>\u03c0<\/jats:italic>could be generated then a consistent estimator of \u03bb \u2261 \u222b<jats:sub><jats:italic>S<\/jats:italic><\/jats:sub><jats:italic>f<\/jats:italic>d\u03c0 can be produced. We further show that under appropriate second moment conditions, a confidence interval for \u03bb can also be derived. This is illustrated with estimating countable sums and integrals with respect to absolutely continuous measures on \u211d<jats:sup><jats:italic>d<\/jats:italic><\/jats:sup>using a simple symmetric random walk on \u2124.<\/jats:p>","DOI":"10.1017\/s0021900200113129","type":"journal-article","created":{"date-parts":[[2016,3,30]],"date-time":"2016-03-30T20:26:57Z","timestamp":1459369617000},"page":"1133-1145","source":"Crossref","is-referenced-by-count":2,"title":["Estimation of integrals with respect to infinite measures using regenerative sequences"],"prefix":"10.1017","volume":"52","author":[{"given":"Krishna B.","family":"Athreya","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Vivekananda","family":"Roy","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"56","published-online":{"date-parts":[[2016,3,30]]},"reference":[{"key":"S0021900200113129_ref6","doi-asserted-by":"publisher","DOI":"10.1287\/opre.23.1.33"},{"key":"S0021900200113129_ref1","volume-title":"Stochastic Simulation: Algorithms and Analysis.","year":"2007"},{"key":"S0021900200113129_ref5","first-page":"167","volume":"46","year":"1992","journal-title":"Amer. 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