{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,21]],"date-time":"2026-04-21T14:42:48Z","timestamp":1776782568082,"version":"3.51.2"},"reference-count":16,"publisher":"American Mathematical Society (AMS)","issue":"246","license":[{"start":{"date-parts":[[2004,8,19]],"date-time":"2004-08-19T00:00:00Z","timestamp":1092873600000},"content-version":"am","delay-in-days":366,"URL":"https:\/\/www.ams.org\/publications\/copyright-and-permissions"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Math. Comp."],"abstract":"<p>\n                    We present and analyze a new randomized algorithm for numerical computation of weighted integrals over the\n                    <italic>unbounded<\/italic>\n                    domain\n                    <inline-formula content-type=\"math\/mathml\">\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"double-struck upper R Superscript d\">\n                        <mml:semantics>\n                          <mml:msup>\n                            <mml:mrow class=\"MJX-TeXAtom-ORD\">\n                              <mml:mi mathvariant=\"double-struck\">R<\/mml:mi>\n                            <\/mml:mrow>\n                            <mml:mi>d<\/mml:mi>\n                          <\/mml:msup>\n                          <mml:annotation encoding=\"application\/x-tex\">\\mathbb {R}^d<\/mml:annotation>\n                        <\/mml:semantics>\n                      <\/mml:math>\n                    <\/inline-formula>\n                    . The algorithm and its desirable theoretical properties are derived based on certain stochastic assumptions about the integrands. It is easy to implement, enjoys\n                    <inline-formula content-type=\"math\/mathml\">\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"upper O left-parenthesis n Superscript negative 1 slash 2 Baseline right-parenthesis\">\n                        <mml:semantics>\n                          <mml:mrow>\n                            <mml:mi>O<\/mml:mi>\n                            <mml:mo stretchy=\"false\">(<\/mml:mo>\n                            <mml:msup>\n                              <mml:mi>n<\/mml:mi>\n                              <mml:mrow class=\"MJX-TeXAtom-ORD\">\n                                <mml:mo>\n                                  \u2212\n                                  \n                                <\/mml:mo>\n                                <mml:mn>1<\/mml:mn>\n                                <mml:mrow class=\"MJX-TeXAtom-ORD\">\n                                  <mml:mo>\/<\/mml:mo>\n                                <\/mml:mrow>\n                                <mml:mn>2<\/mml:mn>\n                              <\/mml:mrow>\n                            <\/mml:msup>\n                            <mml:mo stretchy=\"false\">)<\/mml:mo>\n                          <\/mml:mrow>\n                          <mml:annotation encoding=\"application\/x-tex\">O(n^{-1\/2})<\/mml:annotation>\n                        <\/mml:semantics>\n                      <\/mml:math>\n                    <\/inline-formula>\n                    convergence rate, and uses only standard random number generators. Numerical results are also included.\n                  <\/p>","DOI":"10.1090\/s0025-5718-03-01564-3","type":"journal-article","created":{"date-parts":[[2004,4,21]],"date-time":"2004-04-21T12:29:08Z","timestamp":1082550548000},"page":"813-825","source":"Crossref","is-referenced-by-count":0,"title":["A Monte Carlo algorithm for weighted integration over \u211d^{\ud835\udd55}"],"prefix":"10.1090","volume":"73","author":[{"given":"Piotr","family":"Gajda","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Youming","family":"Li","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Leszek","family":"Plaskota","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Grzegorz","family":"Wasilkowski","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"14","published-online":{"date-parts":[[2003,8,19]]},"reference":[{"key":"1","unstructured":"R.E. Caflisch and W. Morokoff, Quasi-Monte Carlo computation of a finance problem, in K.T. Fang and F.J. Hickernell, eds., Workshop on Quasi-Monte Carlo Methods and Their Applications, 1996, pp.15\u201330."},{"key":"2","doi-asserted-by":"crossref","unstructured":"R.E. Caflisch, W. Morokoff and A.B. Owen, Valuation of mortgage backed securities using Brownian bridges to reduce effective dimension, J. Comp. Finance, 1996, 1, pp.27\u201346.","DOI":"10.21314\/JCF.1997.005"},{"key":"3","isbn-type":"print","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4613-8643-8","volume-title":"Nonuniform random variate generation","author":"Devroye, Luc","year":"1986","ISBN":"https:\/\/id.crossref.org\/isbn\/0387963057"},{"issue":"213","key":"4","doi-asserted-by":"publisher","first-page":"203","DOI":"10.1090\/S0025-5718-96-00696-5","article-title":"Maximally equidistributed combined Tausworthe generators","volume":"65","author":"L\u2019Ecuyer, Pierre","year":"1996","journal-title":"Math. Comp.","ISSN":"https:\/\/id.crossref.org\/issn\/0025-5718","issn-type":"print"},{"issue":"3","key":"5","doi-asserted-by":"publisher","first-page":"543","DOI":"10.1007\/BF02109835","article-title":"On the theory of estimates of the Monte Carlo method that are connected with a \u201crandom walk on spheres\u201d","volume":"36","author":"Elepov, B. S.","year":"1995","journal-title":"Sibirsk. Mat. Zh.","ISSN":"https:\/\/id.crossref.org\/issn\/0037-4474","issn-type":"print"},{"issue":"2-5","key":"6","doi-asserted-by":"publisher","first-page":"287","DOI":"10.1016\/S0378-4754(98)00105-0","article-title":"Stochastic methods for multiple integrals over unbounded regions","volume":"47","author":"Genz, Alan","year":"1998","journal-title":"Math. Comput. Simulation","ISSN":"https:\/\/id.crossref.org\/issn\/0378-4754","issn-type":"print"},{"key":"7","doi-asserted-by":"publisher","first-page":"361","DOI":"10.2307\/2003589","article-title":"A modified Monte-Carlo quadrature","volume":"20","author":"Haber, Seymour","year":"1966","journal-title":"Math. Comp.","ISSN":"https:\/\/id.crossref.org\/issn\/0025-5718","issn-type":"print"},{"key":"8","doi-asserted-by":"publisher","first-page":"388","DOI":"10.2307\/2003241","article-title":"A modified Monte-Carlo quadrature. II","volume":"21","author":"Haber, Seymour","year":"1967","journal-title":"Math. Comp.","ISSN":"https:\/\/id.crossref.org\/issn\/0025-5718","issn-type":"print"},{"key":"9","unstructured":"P. Mathe and G. Wei, Quasi-Monte Carlo integration over \u211d^{\ud835\udd55}, to appear."},{"key":"10","doi-asserted-by":"crossref","unstructured":"M. Matsumoto and T. Nishimura, Mersenne Twister: a 623-dimensionally equidistributed uniform pseudorandom number generator, ACM Transactions on Modeling and Computer Simulation, 1 (1998), pp.3-30.","DOI":"10.1145\/272991.272995"},{"key":"11","doi-asserted-by":"crossref","unstructured":"A. Papageorgiou and J.F. Traub, Faster Evaluation of Multidimensional Integrals, Computers in Physics, Nov.\/Dec. 1997, pp.574\u2013578.","DOI":"10.1063\/1.168616"},{"key":"12","series-title":"Publications of the Newton Institute","isbn-type":"print","volume-title":"Mathematics of derivative securities","volume":"15","year":"1997","ISBN":"https:\/\/id.crossref.org\/isbn\/0521584248"},{"key":"13","doi-asserted-by":"crossref","unstructured":"L. Plaskota, K. Ritter, and G.W. Wasilkowski, Average case complexity of weighted integration and approximation over \u211d^{\ud835\udd55} with isotropic weight, in K.T. Fang, J.F. Hickernell, and H. Niederreiter, eds., Monte Carlo and Quasi Monte Carlo 2000, Hong-Kong, Springer 2002, pp.446\u2013459.","DOI":"10.1007\/978-3-642-56046-0_31"},{"key":"14","unstructured":"L. Plaskota, K. Ritter, and G.W. Wasilkowski, Optimal designs for weighted approximation and integration of stochastic processes on [0,\u221e), 2002, submitted."},{"key":"15","doi-asserted-by":"crossref","unstructured":"S. Tezuka, \u201cUniform Random Numbers: Theory and Practice,\" Kluwer Academic Publishers, Boston, 1995.","DOI":"10.1007\/978-1-4615-2317-8"},{"key":"16","doi-asserted-by":"crossref","unstructured":"R. M. Ziff, Four-tap shift-register-sequence random-number generators, Computers in Physics, Jul\/Aug 1998, pp.385\u2013392.","DOI":"10.1063\/1.168692"}],"container-title":["Mathematics of Computation"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/www.ams.org\/mcom\/2004-73-246\/S0025-5718-03-01564-3\/S0025-5718-03-01564-3.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"},{"URL":"https:\/\/www.ams.org\/mcom\/2004-73-246\/S0025-5718-03-01564-3\/S0025-5718-03-01564-3.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,4,21]],"date-time":"2026-04-21T13:44:10Z","timestamp":1776779050000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.ams.org\/mcom\/2004-73-246\/S0025-5718-03-01564-3\/"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2003,8,19]]},"references-count":16,"journal-issue":{"issue":"246","published-print":{"date-parts":[[2004,4]]}},"alternative-id":["S0025-5718-03-01564-3"],"URL":"https:\/\/doi.org\/10.1090\/s0025-5718-03-01564-3","archive":["CLOCKSS","Portico"],"relation":{},"ISSN":["1088-6842","0025-5718"],"issn-type":[{"value":"1088-6842","type":"electronic"},{"value":"0025-5718","type":"print"}],"subject":[],"published":{"date-parts":[[2003,8,19]]}}}