{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,26]],"date-time":"2026-08-26T05:17:22Z","timestamp":1787721442637,"version":"build-2784847793"},"reference-count":25,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"2","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["SIAM J. Sci. Comput."],"published-print":{"date-parts":[[2006,1]]},"abstract":"<jats:p>Efficient numerical algorithms are proposed for a class of forward-backward stochastic differential equations (FBSDEs) connected with semilinear parabolic partial differential equations. As in [J. Douglas, Jr., J. Ma, and P. Protter, Ann. Appl. Probab., 6 (1996), pp. 940-968], the algorithms are based on the known four-step scheme for solving FBSDEs. The corresponding semilinear parabolic equation is solved by layer methods which are constructed by means of a probabilistic approach. The derivatives of the solution u of the semilinear equation are found by finite differences. The forward equation is simulated by mean-square methods of order 1\/2 and 1. Corresponding convergence theorems are proved. Along with the algorithms for FBSDEs on a fixed finite time interval, we also construct algorithms for FBSDEs with random terminal time. The results obtained are supported by numerical experiments.<\/jats:p>","DOI":"10.1137\/040614426","type":"journal-article","created":{"date-parts":[[2006,4,25]],"date-time":"2006-04-25T21:04:44Z","timestamp":1145999084000},"page":"561-582","source":"Crossref","is-referenced-by-count":75,"title":["Numerical Algorithms for Forward-Backward Stochastic Differential Equations"],"prefix":"10.1137","volume":"28","author":[{"given":"G. N.","family":"Milstein","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"M. 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