{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,2]],"date-time":"2026-01-02T07:42:04Z","timestamp":1767339724200},"reference-count":15,"publisher":"Walter de Gruyter GmbH","issue":"2","funder":[{"DOI":"10.13039\/501100001691","name":"Japan Society for the Promotion of Science","doi-asserted-by":"publisher","award":["16K13773"],"award-info":[{"award-number":["16K13773"]}],"id":[{"id":"10.13039\/501100001691","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2019,6,1]]},"abstract":"<jats:title>Abstract<\/jats:title>\n               <jats:p>This paper proposes a new third-order discretization algorithm for multidimensional It\u00f4 stochastic differential equations driven by Brownian motions.\nThe scheme is constructed by the Euler\u2013Maruyama scheme with a stochastic weight given by polynomials of Brownian motions, which is simply implemented by a Monte Carlo method.\nThe method of Watanabe distributions on Wiener space is effectively applied in the computation of the polynomial weight of Brownian motions.\nNumerical examples are shown to confirm the accuracy of the scheme.<\/jats:p>","DOI":"10.1515\/mcma-2019-2036","type":"journal-article","created":{"date-parts":[[2019,6,13]],"date-time":"2019-06-13T09:11:57Z","timestamp":1560417117000},"page":"97-120","source":"Crossref","is-referenced-by-count":17,"title":["A third-order weak approximation of multidimensional It\u00f4 stochastic differential equations"],"prefix":"10.1515","volume":"25","author":[{"given":"Riu","family":"Naito","sequence":"first","affiliation":[{"name":"Hitotsubashi University , Tokyo , Japan"}]},{"given":"Toshihiro","family":"Yamada","sequence":"additional","affiliation":[{"name":"Hitotsubashi University , Tokyo , Japan"}]}],"member":"374","published-online":{"date-parts":[[2019,5,24]]},"reference":[{"key":"2023040101340307705_j_mcma-2019-2036_ref_001_w2aab3b7b4b1b6b1ab1b7b1Aa","unstructured":"J.-M.  Bismut,\nLarge Deviations and the Malliavin Calculus,\nProgr. Math. 45,\nBirkh\u00e4user, Boston, 1984."},{"key":"2023040101340307705_j_mcma-2019-2036_ref_002_w2aab3b7b4b1b6b1ab1b7b2Aa","unstructured":"N.  Ikeda and S.  Watanabe,\nStochastic Differential Equations and Diffusion Processes, 2nd ed.,\nNorth-Holland Math. Libr. 24,\nNorth-Holland, Amsterdam, 1989."},{"key":"2023040101340307705_j_mcma-2019-2036_ref_003_w2aab3b7b4b1b6b1ab1b7b3Aa","unstructured":"P. E.  Kloeden and E.  Platen,\nNumerical Solution of Stochastic Differential Equations,\nSpringer, Berlin, 1999."},{"key":"2023040101340307705_j_mcma-2019-2036_ref_004_w2aab3b7b4b1b6b1ab1b7b4Aa","unstructured":"S.  Kusuoka,\nApproximation of expectation of diffusion process and mathematical finance,\nTaniguchi Conference on Mathematics Nara \u201998,\nAdv. Stud. Pure Math. 31,\nMathematical Society of Japan, Tokyo (2001), 147\u2013165."},{"key":"2023040101340307705_j_mcma-2019-2036_ref_005_w2aab3b7b4b1b6b1ab1b7b5Aa","doi-asserted-by":"crossref","unstructured":"S.  Kusuoka and D.  Stroock,\nApplications of the Malliavin calculus. I,\nStochastic Analysis (Katata\/Kyoto 1982),\nNorth-Holland Math. Libr. 32,\nNorth-Holland, Amsterdam (1984), 271\u2013306.","DOI":"10.1016\/S0924-6509(08)70397-0"},{"key":"2023040101340307705_j_mcma-2019-2036_ref_006_w2aab3b7b4b1b6b1ab1b7b6Aa","doi-asserted-by":"crossref","unstructured":"G.  Maruyama,\nContinuous Markov processes and stochastic equations,\nRend. Circ. Mat. Palermo (2) 4 (1955), 48\u201390.\n10.1007\/BF02846028","DOI":"10.1007\/BF02846028"},{"key":"2023040101340307705_j_mcma-2019-2036_ref_007_w2aab3b7b4b1b6b1ab1b7b7Aa","unstructured":"D.  Nualart,\nThe Malliavin Calculus and Related Topics,\nSpringer, Berlin, 2006."},{"key":"2023040101340307705_j_mcma-2019-2036_ref_008_w2aab3b7b4b1b6b1ab1b7b8Aa","doi-asserted-by":"crossref","unstructured":"Y.  Shinozaki,\nConstruction of a third-order K-scheme and its application to financial models,\nSIAM J. Financial Math. 8 (2017), no. 1, 901\u2013932.\n10.1137\/16M1067986","DOI":"10.1137\/16M1067986"},{"key":"2023040101340307705_j_mcma-2019-2036_ref_009_w2aab3b7b4b1b6b1ab1b7b9Aa","doi-asserted-by":"crossref","unstructured":"A.  Takahashi and T.  Yamada,\nAn asymptotic expansion with push-down of Malliavin weights,\nSIAM J. Financial Math. 3 (2012), no. 1, 95\u2013136.\n10.1137\/100807624","DOI":"10.1137\/100807624"},{"key":"2023040101340307705_j_mcma-2019-2036_ref_010_w2aab3b7b4b1b6b1ab1b7c10Aa","doi-asserted-by":"crossref","unstructured":"A.  Takahashi and T.  Yamada,\nA weak approximation with asymptotic expansion and multidimensional Malliavin weights,\nAnn. Appl. Probab. 26 (2016), no. 2, 818\u2013856.\n10.1214\/15-AAP1105","DOI":"10.1214\/15-AAP1105"},{"key":"2023040101340307705_j_mcma-2019-2036_ref_011_w2aab3b7b4b1b6b1ab1b7c11Aa","doi-asserted-by":"crossref","unstructured":"T.  Yamada,\nA higher order weak approximation scheme of multidimensional stochastic differential equations using Malliavin weights,\nJ. Comput. Appl. Math. 321 (2017), 427\u2013447.\n10.1016\/j.cam.2017.03.001","DOI":"10.1016\/j.cam.2017.03.001"},{"key":"2023040101340307705_j_mcma-2019-2036_ref_012_w2aab3b7b4b1b6b1ab1b7c12Aa","doi-asserted-by":"crossref","unstructured":"T.  Yamada,\nAn arbitrary high order weak approximation of SDE and Malliavin Monte Carlo: Analysis of probability distribution functions,\nSIAM J. Numer. Anal. 57 (2019), no. 2, 563\u2013591.\n10.1137\/17M114412X","DOI":"10.1137\/17M114412X"},{"key":"2023040101340307705_j_mcma-2019-2036_ref_013_w2aab3b7b4b1b6b1ab1b7c13Aa","doi-asserted-by":"crossref","unstructured":"T.  Yamada and K.  Yamamoto,\nA second-order discretization with Malliavin weight and Quasi-Monte Carlo method for option pricing,\nQuant. Finance 18 (2018), 10.1080\/14697688.2018.1430371.","DOI":"10.2139\/ssrn.3012898"},{"key":"2023040101340307705_j_mcma-2019-2036_ref_014_w2aab3b7b4b1b6b1ab1b7c14Aa","doi-asserted-by":"crossref","unstructured":"T.  Yamada and K.  Yamamoto,\nA second-order weak approximation of SDEs using a Markov chain without L\u00e9vy area simulation,\nMonte Carlo Methods Appl. 24 (2018), no. 4, 289\u2013308.\n10.1515\/mcma-2018-2024","DOI":"10.1515\/mcma-2018-2024"},{"key":"2023040101340307705_j_mcma-2019-2036_ref_015_w2aab3b7b4b1b6b1ab1b7c15Aa","doi-asserted-by":"crossref","unstructured":"T.  Yamada and K.  Yamamoto,\nSecond order discretization of Bismut\u2013Elworthy-Li formula: Application to sensitivity analysis,\nSIAM\/ASA J. Uncertain. 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