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The scheme is explicitly constructed by polynomials of Brownian motions up to second order, and any discrete moment-matched random variables or the L\u00e9vy area simulation method are not used. The required number of random variables is still\n                    <jats:italic>d<\/jats:italic>\n                    in one-step simulation of the implementation of the scheme. In the Markov chain, a correction term with Lie bracket of vector fields associated with SDEs appears as the cost of not using moment-matched random variables.\n                  <\/jats:p>","DOI":"10.1515\/mcma-2018-2024","type":"journal-article","created":{"date-parts":[[2018,10,27]],"date-time":"2018-10-27T05:08:14Z","timestamp":1540616894000},"page":"289-308","source":"Crossref","is-referenced-by-count":5,"title":["A second-order weak approximation of SDEs using a Markov chain without L\u00e9vy area simulation"],"prefix":"10.1515","volume":"24","author":[{"given":"Toshihiro","family":"Yamada","sequence":"first","affiliation":[{"name":"Hitotsubashi University , Tokyo , Japan"}]},{"given":"Kenta","family":"Yamamoto","sequence":"additional","affiliation":[{"name":"MUFG Bank , Tokyo , Japan"}]}],"member":"374","published-online":{"date-parts":[[2018,10,23]]},"reference":[{"key":"2023040101333948454_j_mcma-2018-2024_ref_001_w2aab3b7b5b1b6b1ab1b4b1Aa","doi-asserted-by":"crossref","unstructured":"L. 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