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Bismut,\nLarge Deviations and the Malliavin Calculus,\nProgr. Math. 45,\nBirkh\u00e4user, Boston, 1984."},{"key":"2023040101440770371_j_mcma-2019-2053_ref_002_w2aab3b7b6b1b6b1ab1b4b2Aa","doi-asserted-by":"crossref","unstructured":"B.  Bouchard, X.  Tan, X.  Warin and Y.  Zou,\nNumerical approximation of BSDEs using local polynomial drivers and branching processes,\nMonte Carlo Methods Appl. 23 (2017), no. 4, 241\u2013263.","DOI":"10.1515\/mcma-2017-0116"},{"key":"2023040101440770371_j_mcma-2019-2053_ref_003_w2aab3b7b6b1b6b1ab1b4b3Aa","doi-asserted-by":"crossref","unstructured":"D.  Crisan and K.  Manolarakis,\nSolving backward stochastic differential equations using the cubature method: Application to nonlinear pricing,\nSIAM J. Financial Math. 3 (2012), no. 1, 534\u2013571.\n10.1137\/090765766","DOI":"10.1137\/090765766"},{"key":"2023040101440770371_j_mcma-2019-2053_ref_004_w2aab3b7b6b1b6b1ab1b4b4Aa","doi-asserted-by":"crossref","unstructured":"D.  Crisan and K.  Manolarakis,\nSecond order discretization of backward SDEs and simulation with the cubature method,\nAnn. Appl. Probab. 24 (2014), no. 2, 652\u2013678.\n10.1214\/13-AAP932","DOI":"10.1214\/13-AAP932"},{"key":"2023040101440770371_j_mcma-2019-2053_ref_005_w2aab3b7b6b1b6b1ab1b4b5Aa","doi-asserted-by":"crossref","unstructured":"M.  Fujii and A.  Takahashi,\nSolving backward stochastic differential equations with quadratic-growth drivers by connecting the short-term expansions,\nStochastic Process. Appl. 129 (2019), no. 5, 1492\u20131532.\n10.1016\/j.spa.2018.05.009","DOI":"10.1016\/j.spa.2018.05.009"},{"key":"2023040101440770371_j_mcma-2019-2053_ref_006_w2aab3b7b6b1b6b1ab1b4b6Aa","doi-asserted-by":"crossref","unstructured":"E.  Gobet and C.  Labart,\nError expansion for the discretization of backward stochastic differential equations,\nStochastic Process. 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Lib. 32,\nNorth-Holland, Amsterdam (1984), 271\u2013306.","DOI":"10.1016\/S0924-6509(08)70397-0"},{"key":"2023040101440770371_j_mcma-2019-2053_ref_010_w2aab3b7b6b1b6b1ab1b4c10Aa","doi-asserted-by":"crossref","unstructured":"R.  Naito and T.  Yamada,\nA third-order weak approximation of multidimensional It\u00f4 stochastic differential equations,\nMonte Carlo Methods Appl. 25 (2019), no. 2, 97\u2013120.\n10.1515\/mcma-2019-2036","DOI":"10.1515\/mcma-2019-2036"},{"key":"2023040101440770371_j_mcma-2019-2053_ref_011_w2aab3b7b6b1b6b1ab1b4c11Aa","unstructured":"D.  Nualart,\nThe Malliavin Calculus and Related Topics,\nSpringer, Berlin, 2006."},{"key":"2023040101440770371_j_mcma-2019-2053_ref_012_w2aab3b7b6b1b6b1ab1b4c12Aa","doi-asserted-by":"crossref","unstructured":"A.  Takahashi and T.  Yamada,\nAn asymptotic expansion with push-down of Malliavin weights,\nSIAM J. 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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":"2023040101440770371_j_mcma-2019-2053_ref_016_w2aab3b7b6b1b6b1ab1b4c16Aa","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":"2023040101440770371_j_mcma-2019-2053_ref_017_w2aab3b7b6b1b6b1ab1b4c17Aa","doi-asserted-by":"crossref","unstructured":"T.  Yamada and K.  Yamamoto,\nSecond order discretization of Bismut\u2013Elworthy\u2013Li formula: Application to sensitivity analysis,\nSIAM\/ASA J. Uncertain. 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