An efficient approximation for stochastic differential equations on the partition ofsymmetricalirst

References

• Billingsley , P. 1979 . Probability and Measure , New York : Wiley .
   Google Scholar
• Clark , J. M. C. 1982 . “ An efficient approximation for a class of stochastic differential equations ” . In In Advances in Filtering and Optimal Stochastic Control , Edited by: Fleming , W. H. and Gorostiza , L. G. Vol. 42 , Mexico : Springer-Verlag .
   Google Scholar
• Clark , J. M. C. 1984 . “ Asymptotically optimal quadrature formulae for stochastic integrals ” . In Proceedings of the 23rd Conference on Decision and Control , 712 – 715 . Nevada, , USA : Las Vegas . IEEE
   Google Scholar
• Clark , J. M. C. and Cameron , R. J. 1980 . “ The maximum rate of convergence of discrete approximations for stochastic differential equations ” . In In Stochastic Differential Systems Filtering and Control , Edited by: Grigelionis , B. Vol. 25 , Vilnius, Lithuania : Springer-Verlag .
   Google Scholar
• Gihman , I. I. and Skorohod , A. V. 1972 . Stochastic Differential Equations , Springer-Verlag .
   Google Scholar
• Gorostiza , L. G. 1980 . Rate of convergence of an approximate solution of stochastic differential equations . Stochastics , 4 ( 85 ) : 267 – 276 .
   Google Scholar
• Gorostiza , L. G. and Griego , R. J. 1980 . Rate of convergence of uniform transport processes to Brownian motion and application to stochastic integrals . Stochastics , 3 ( 85 ) : 291 – 303 .
   Google Scholar
• It , K. and Mckean , H.P. 1965 . Diffusion Processes and Their Sample Paths , Springer-Verlag .
   Google Scholar
• Liptser , R. S. and Shiryayev , A. N. 1977 . Statistics of Random Processes I General Theory , Springer-Verlag .
   Google Scholar
• Mikulevicius , R. and Platen , E. 1986 . Rate of convergence of the Euler approximation for diffusion processes , Berlin : Karl Weierstrass Institut fur Mathematik der Akademie der Wissenschaften der DDR . Preprint P-MATH-38/86
   Google Scholar
• Milshtein , G. N. 1974 . Approximate integration of stochastic differential equations . Th. Prob. Appl , 19 : 557 – 562 .
   Google Scholar
• Milshtein , G. N. 1978 . A method of second-order accuracy integration of stochastic differential equations . Th. Prob. Appl , 23 : 396 – 401 .
   Web of Science ®Google Scholar
• Milshtein , G. N. 1985 . Weak approximation of solutions of systems of stochastic differential equations . Th. Prob. Appl , 30 : 750 – 766 .
   Web of Science ®Google Scholar
• Newton , N. J. 1986 . An asymptotically efficient difference formula for solving stochastic differential equations . Stochastics , 19 : 175 – 206 .
   Google Scholar
• Pardoux , E. and Talay , D. 1985 . Discretization and simulation of stochastic differential equations . Acta Applicandae Mathematicae , 3 : 23 – 47 .
   Web of Science ®Google Scholar
• Talay , D. 1984 . “ Efficient numerical schemes for the approximation of expectations of functionals of S.D.E ” . In In Filtering and Control of Random Processes , Edited by: Korezlioglu , H. , Mazziotto , G. and Szpirglas , J. Vol. 61 , 294 – 313 . Paris : Springer-Verlag .
   Google Scholar
• Wagner , W. “ Unbiased Monte Carlo estimators for functionals of weak solutions of stochastic differential equations ” . In Weierstrass Institut fur Mathematik der Akademie der Wissenschaften der DDR , Berlin : Karl . Preprint P-MATH-30/87; Submitted to Stochastics
   Google Scholar
• Wonham , W. M. 1965 . Some applications of stochastic differential equations to optimal nonlinear filtering . J. SIAM Control , 2 : 347 – 369 .
   Google Scholar
• Zakai , M. 1969 . On the optimal filtering of diffusion processes . Z. Wahr. Geb , 11 : 230 – 243 .
   Web of Science ®Google Scholar