The ordinary differential equation approach to asymptotically efficient schemes for solution of stochastic differential equations

Fabienne Castell; Jessica Gaines

Annales de l'I.H.P. Probabilités et statistiques (1996)

  • Volume: 32, Issue: 2, page 231-250
  • ISSN: 0246-0203

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Castell, Fabienne, and 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 32.2 (1996): 231-250. <http://eudml.org/doc/77534>.

@article{Castell1996,
author = {Castell, Fabienne, Gaines, Jessica},
journal = {Annales de l'I.H.P. Probabilités et statistiques},
keywords = {numerical approximation; strong solutions of stochastic differential equations; noncommutative Lie algebra; multidimensional Brownian path; asymptotic efficiency},
language = {eng},
number = {2},
pages = {231-250},
publisher = {Gauthier-Villars},
title = {The ordinary differential equation approach to asymptotically efficient schemes for solution of stochastic differential equations},
url = {http://eudml.org/doc/77534},
volume = {32},
year = {1996},
}

TY - JOUR
AU - Castell, Fabienne
AU - Gaines, Jessica
TI - The ordinary differential equation approach to asymptotically efficient schemes for solution of stochastic differential equations
JO - Annales de l'I.H.P. Probabilités et statistiques
PY - 1996
PB - Gauthier-Villars
VL - 32
IS - 2
SP - 231
EP - 250
LA - eng
KW - numerical approximation; strong solutions of stochastic differential equations; noncommutative Lie algebra; multidimensional Brownian path; asymptotic efficiency
UR - http://eudml.org/doc/77534
ER -

References

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  2. [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. Zbl0726.60056MR1101258
  3. [3] G. Ben Arous, Flots et séries de Taylor stochastiques, Probab. Theory Related Fields, Vol. 81, 1989, pp. 29-77. Zbl0639.60062MR981567
  4. [4] F. Castell, Asymptotic expansion of stochastic flows, Probab. Theory Related Fields, Vol. 96, 1993, pp. 225-239. Zbl0794.60054MR1227033
  5. [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. Zbl0507.93072MR794499
  6. [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. MR609181
  7. [7] J.G. Gaines, The algebra of iterated stochastic integrals. To appear in Stochastics and Stochastic Reports. Zbl0827.60038MR1785003
  8. [8] J.G. Gaines and T.J. Lyons, Random generation of stochastic area integrals. To appear in SIAM J. of Applied Math. Zbl0805.60052MR1284705
  9. [9] Y.Z. Hu, Série de Taylor stochastique et formule de Campbell-Haussdorff, d'après Ben Arous, inSéminaire de ProbabilitésXXV, J. Azema, P. A. Meyer, and M. Yor, eds., no. 1485 in Lecture Notes in Mathematics, Springer-Verlag, 1991/92, pp. 579-586. Zbl0766.60069MR1232020
  10. [10] P.E. Kloeden and E. Platen, Stratonovich and Itô stochastic Taylor expansions, Math. Nachr., Vol. 151, 1991, pp. 33-50. Zbl0731.60050MR1121195
  11. [11] P.E. Kloeden and E. Platen, Numerical Solution of Stochastic Differential Equations, Vol. 23 of Applications of Mathematics, Springer-Verlag, 1992. Zbl0752.60043MR1214374
  12. [12] N.J. Newton, An asymptotically efficient difference formula for solving stochastic differential equations, Stochastics, Vol. 19, 1986, pp. 175-206. Zbl0618.60053MR870619
  13. [13] N.J. Newton, Asymptotically efficient Runge-Kutta methods for a class of Itô and Stratonovich equations, SIAMJ. of Applied Mathematics, Vol. 51, 1991, pp. 542-567. Zbl0724.65135MR1095034
  14. [14] E. Pardoux and D. Talay, Discretization and simulation of stochastic differential equations, Acta Appl. Math., Vol. 3, 1985, pp. 23-47. Zbl0554.60062MR773336
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