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A TAYLOR APPROXIMATION METHOD OF STOCHASTIC INTEGRO-DIFFERENTIAL EQUATIONS

A TAYLOR APPROXIMATION METHOD OF STOCHASTIC INTEGRO-DIFFERENTIAL EQUATIONS
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摘要 In this paper, we formulate a general framework of an analytic approximation of the solutions to some It o stochastic integro-differential equations defined on sub-intervals of an arbitrary part of the time-interval [0,1] and connected at successive division points. The integral parts and coefficients of the equation are approximated by their Taylor polynomial which series up to arbitrary derivatives. The suggested approximations converge to the initial solution in the Lp-th norm with some order. In this paper, we formulate a general framework of an analytic approximation of the solutions to some It o stochastic integro-differential equations defined on sub-intervals of an arbitrary part of the time-interval [0,1] and connected at successive division points. The integral parts and coefficients of the equation are approximated by their Taylor polynomial which series up to arbitrary derivatives. The suggested approximations converge to the initial solution in the Lp-th norm with some order.
作者 Weiguo Liu Xinmei Liu
机构地区 Dept.of Probability and Statistics
出处 《Annals of Differential Equations》 2013年第2期167-176,共10页 微分方程年刊（英文版）
关键词 analytic approximation stochastic integro-differential equations Taylor expansion Lp -convergence analytic approximation stochastic integro-differential equations Taylor expansion Lp -convergence
分类号 O211.63 [理学—概率论与数理统计]
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参考文献11

  • 1Svetlana Jankovic,Dejan Ilic.ONE LINEAR ANALYTIC APPROXIMATION FOR STOCHASTIC INTEGRODIFFERENTIAL EQUATIONS[J].Acta Mathematica Scientia,2010,30(4):1073-1085. 被引量：1
  • 2Lazhar Bougoffa,Randolph C Rach,Abdelaziz Mennouni.An approximate method for solving a class of weakly-singular Volterra integro-differential equa-tions[].Journal of Applied Mathematics.2011
  • 3Svetlana Jankovic,Maja Vasilova,Marij Krstic.Some analytic approximationsfor neutral stochastic functional differential equations[].Applied Mathemat-ics and Computation.2010
  • 4Jankovic S,Ilic D.An analytic approximation of solutions of stochastic differential equations[].Computers and Mathematicswith Application.2004
  • 5X. Mao.Stochastic Differential Equations and Applications[].Horwood Series in Mathema- tics & Applications.1997
  • 6M.G. Murge,B.G. Pachpatte.Succesive approximations for solutions of second order stochastic integro-differential equations of Ito type[].Indian Journal of Pure and Applied Mathematics.1990
  • 7Jovanovi M,Jankovi Sv.On perturbed nonlinear Ito type stochastic integrodierential equations[].Journal of Mathematical Analysis and Applications.2002
  • 8Kristian Debrabant,Andreas Rler.Continuous weak approximation for stochastic differential equations[].Journal of Computational and Applied Mathematics.2008
  • 9Xuerong Mao,Chenggui Yuan,G Yin.Approximations of Euler-Maruyama type for stochastic differential equations with Markovian switching, under non-Lipschitz conditions[].Journal of Computational and Applied Mathematics.2007
  • 10Marija Milosˇevic,Miljana Jovanovic.An application of Taylor series in the ap-proximation of solutions to stochastic differential equations with time-dependentdelay[].Journal of Computational and Applied Mathematics.2011

二级参考文献18

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Annals of Differential Equations
2013年 第2期

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