The ordinary differential equation approach to asymptotically efficient schemes for solution of stochastic differential equations
Annales de l'I.H.P. Probabilités et statistiques, Tome 32 (1996) no. 2, pp. 231-250. 
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     author = {Castell, Fabienne and Gaines, Jessica},
     title = {The ordinary differential equation approach to asymptotically efficient schemes for solution of stochastic differential equations},
     journal = {Annales de l'I.H.P. Probabilit\'es et statistiques},
     pages = {231--250},
     publisher = {Gauthier-Villars},
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     number = {2},
     year = {1996},
     mrnumber = {1386220},
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     url = {http://archive.numdam.org/item/AIHPB_1996__32_2_231_0/}
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Castell, Fabienne; Gaines, Jessica. The ordinary differential equation approach to asymptotically efficient schemes for solution of stochastic differential equations. Annales de l'I.H.P. Probabilités et statistiques, Tome 32 (1996) no. 2, pp. 231-250. http://archive.numdam.org/item/AIHPB_1996__32_2_231_0/

[1] R. Azencott, Formule de Taylor stochastique et développement asymptotique d'intégrales de Feynmann, in Séminaire de Probabilités XVI, Supplément: Géométrie différentielle stochastique, Springer-Verlag, 1980/81, pp. 237-284. | Numdam | MR | Zbl

[2] V. Bally, On the connection between the Malliavin covariance matrix and Hörmander's condition, Journal of Functional Analysis, Vol. 96, 1991, pp. 219-255. | MR | Zbl

[3] G. Ben Arous, Flots et séries de Taylor stochastiques, Probab. Theory Related Fields, Vol. 81, 1989, pp. 29-77. | MR | Zbl

[4] F. Castell, Asymptotic expansion of stochastic flows, Probab. Theory Related Fields, Vol. 96, 1993, pp. 225-239. | MR | Zbl

[5] J.M.C. Clark, An efficient approximation for a class of stochastic differential equations, in Advances in filtering and optimal stochastic control, Proceedings of IFIP-WG7/1 Working Conference, Cocoyoc, Mexico, 1982, W. H. Fleming and L. G. Gorostiza, eds., no. 42 in Lecture Notes in Control and Information Sciences, Springer-Verlag, Berlin, 1982. | MR | Zbl

[6] J.M.C. Clark and R.J. Cameron, The maximum rate of convergence of discrete approximations for stochastic differential equations, in Stochastic Differential Systems, B. Grigelionis, ed., no. 25 in Lecture Notes in Control and Information Sciences, Springer-Verlag, Berlin, 1980. | MR

[7] J.G. Gaines, The algebra of iterated stochastic integrals. To appear in Stochastics and Stochastic Reports. | MR | Zbl

[8] J.G. Gaines and T.J. Lyons, Random generation of stochastic area integrals. To appear in SIAM J. of Applied Math. | MR | Zbl

[9] Y.Z. Hu, Série de Taylor stochastique et formule de Campbell-Haussdorff, d'après Ben Arous, in Séminaire de Probabilités XXV, J. Azema, P. A. Meyer, and M. Yor, eds., no. 1485 in Lecture Notes in Mathematics, Springer-Verlag, 1991/92, pp. 579-586. | Numdam | MR | Zbl

[10] P.E. Kloeden and E. Platen, Stratonovich and Itô stochastic Taylor expansions, Math. Nachr., Vol. 151, 1991, pp. 33-50. | MR | Zbl

[11] P.E. Kloeden and E. Platen, Numerical Solution of Stochastic Differential Equations, Vol. 23 of Applications of Mathematics, Springer-Verlag, 1992. | MR | Zbl

[12] N.J. Newton, An asymptotically efficient difference formula for solving stochastic differential equations, Stochastics, Vol. 19, 1986, pp. 175-206. | MR | Zbl

[13] N.J. Newton, Asymptotically efficient Runge-Kutta methods for a class of Itô and Stratonovich equations, SIAM J. of Applied Mathematics, Vol. 51, 1991, pp. 542-567. | MR | Zbl

[14] E. Pardoux and D. Talay, Discretization and simulation of stochastic differential equations, Acta Appl. Math., Vol. 3, 1985, pp. 23-47. | MR | Zbl

[15] L.C.G. Rogers and D. Williams, Diffusions, Markov Processes and Martingales 2, Itô Calculus, John Wiley and Sons, 1987. | MR | Zbl

[16] D. Talay, Simulation and numerical analysis of stochastic differential systems: A review, Tech. Report 1313, INRIA, 1990.