Discretization of stochastic differential equations by the product expansion for the chen series

References

• Ben Arous , G. 1989 . Flots et séeries de Taylor stochastiques . Probab. Theory Relat. Fields , 81 : 29 – 77 .
   Web of Science ®Google Scholar
• Castell , F. 1993 . Asymptotic expansion of stochastic flows . Probab. Theory Relat. Fields , 96 : 225 – 239 .
   Web of Science ®Google Scholar
• Castel , F. and Gaines , J.G. 1993 . The ordinary differential equation approach to asymptotically efficient schemes for solution of stochastic differential equations . Annales de l'Institut H. Poincare , 96 to appear
   Google Scholar
• Gaines , J.G. 1994 . The algebra of iterated stochastic integrals . Stochastics and Stochastics Reports , 49 : 169 – 179 .
   Google Scholar
• Gaines , J.G. and Lyons , T.J. 1994 . Random generation of stochastic area integrals . SIAM J. Appl. Math. , 54 : 1132 – 1146 .
   Web of Science ®Google Scholar
• Hu , Y.Z. 1992 . “ Série de Taylor stochastique et formule de Campbell-Hausdorff, d'aprés Ben Arous ” . In Séminaire de Probabilités XXVI , Lecture Notes in Math Vol. 1526 , 579 – 586 . Berlin : Springer-Verlag .
   Google Scholar
• Kloeden , P.E. and Platen , E. 1992 . “ Numerical Solution of Stochastic Differential Equations ” . Berlin : Springer-Verlag .
   Google Scholar
• Li , C.W. Almost sure convergence of stochastic differential equations of jump-diffusion type . Seminar on Stochastic Analysis Random Fields and Applications,Progress in Probability . Vol. 36 , pp. 187 – 197 . Basel : Birkhäuser Verlag .
   Google Scholar
• Li , C.W. and Liu , X.Q. Strong derivative free schemes for stochastic dynamical systems . 5th International Conference on Advances in Communication and Control Proceedings . pp. 823 – 834 .
   Google Scholar
• Milstein , G.N. 1995 . “ Numerical Integration of Stochastic Differential Equations ” . Sverdlovsk : Ural State University Press . revised translation, Kluwer Academic Publishers, Dordrecht 1988
   Google Scholar
• Newton , N.J. 1986 . An asymptotically efficient difference formula for solving stochastic differential equations . Stochastics , 19 : 175 – 206 .
   Google Scholar
• Newton , N.J. 1990 . An efficient approximation for stochastic differential equations on the partition of symmetrical first passage times . Stochastics and Stochastics Reports , 29 : 227 – 258 .
   Google Scholar
• Newton , N.J. 1991 . Asymptotically efficient Runge-Kutta methods for a class of Ito and Stratonovich equations . SIAM J. Appl. Math. , 51 : 542 – 567 .
   Web of Science ®Google Scholar
• Pardoux , E. and Talay , D. 1985 . Discretization and simulation of stochastic differential equations . Acta Appliandae Mathematicae , 3 : 23 – 47 .
   Web of Science ®Google Scholar
• Sussmann , H.J. 1986 . “ A product expansion for the Chen series ” . In Theory andApplications of Nonlinear Control Systems , Edited by: Byrnes , C.I. and Lindquist , A. 323 – 335 . North-Holland .
   Google Scholar
• Sussmann , H.J. 1988 . “ Product expansions of exponential Lie series and the discretization of stochastic differential equations ” . In Stochastic Differential Systems, Stochastic Control Theory and Applications , Edited by: Fleming , W. and Lions , P.L. 563 – 582 . Springer-Verlag .
   Google Scholar
• Talay , D. 1983 . Résolution trajectorielle et analyse numérique des équations différentielles stochastiques . Stochastics , 9 : 275 – 306 .
   Google Scholar
• Talay , D. 1995 . “ Simulation of stochastic differential systems ” . In Probabilistic Methods in Applied Physics , Lecture Notes in Physics Edited by: Krée , P. and Wedig , W. Berlin : Springer-Verlag .
   Google Scholar