The ordinary differential equation approach to asymptotically efficient schemes for solution of stochastic differential equations
Annales de l'I.H.P. Probabilités et statistiques, Volume 32 (1996) no. 2, p. 231-250
@article{AIHPB_1996__32_2_231_0,
     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},
     publisher = {Gauthier-Villars},
     volume = {32},
     number = {2},
     year = {1996},
     pages = {231-250},
     zbl = {0851.60054},
     mrnumber = {1386220},
     language = {en},
     url = {http://www.numdam.org/item/AIHPB_1996__32_2_231_0}
}
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, Volume 32 (1996) no. 2, pp. 231-250. http://www.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 658728 | Zbl 0484.60064

[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 1101258 | Zbl 0726.60056

[3] G. Ben Arous, Flots et séries de Taylor stochastiques, Probab. Theory Related Fields, Vol. 81, 1989, pp. 29-77. | MR 981567 | Zbl 0639.60062

[4] F. Castell, Asymptotic expansion of stochastic flows, Probab. Theory Related Fields, Vol. 96, 1993, pp. 225-239. | MR 1227033 | Zbl 0794.60054

[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 794499 | Zbl 0507.93072

[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 609181

[7] J.G. Gaines, The algebra of iterated stochastic integrals. To appear in Stochastics and Stochastic Reports. | MR 1785003 | Zbl 0827.60038

[8] J.G. Gaines and T.J. Lyons, Random generation of stochastic area integrals. To appear in SIAM J. of Applied Math. | MR 1284705 | Zbl 0805.60052

[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 1232020 | Zbl 0766.60069

[10] P.E. Kloeden and E. Platen, Stratonovich and Itô stochastic Taylor expansions, Math. Nachr., Vol. 151, 1991, pp. 33-50. | MR 1121195 | Zbl 0731.60050

[11] P.E. Kloeden and E. Platen, Numerical Solution of Stochastic Differential Equations, Vol. 23 of Applications of Mathematics, Springer-Verlag, 1992. | MR 1214374 | Zbl 0752.60043

[12] N.J. Newton, An asymptotically efficient difference formula for solving stochastic differential equations, Stochastics, Vol. 19, 1986, pp. 175-206. | MR 870619 | Zbl 0618.60053

[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 1095034 | Zbl 0724.65135

[14] E. Pardoux and D. Talay, Discretization and simulation of stochastic differential equations, Acta Appl. Math., Vol. 3, 1985, pp. 23-47. | MR 773336 | Zbl 0554.60062

[15] L.C.G. Rogers and D. Williams, Diffusions, Markov Processes and Martingales 2, Itô Calculus, John Wiley and Sons, 1987. | MR 921238 | Zbl 0627.60001

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