• 论文 • 上一篇    

一类随机分数阶微分方程隐式Euler方法的弱收敛性与弱稳定性

王文强, 孙晓莉   

  1. 湘潭大学数学与计算科学学院, 湖南 湘潭 411105
  • 收稿日期:2013-12-23 出版日期:2014-06-15 发布日期:2014-05-29
  • 通讯作者: 王文强,Email:wwq@xtu.edu.cn.
  • 基金资助:

    国家自然科学基金(11271311、11171352)资助项目.

王文强, 孙晓莉. 一类随机分数阶微分方程隐式Euler方法的弱收敛性与弱稳定性[J]. 数值计算与计算机应用, 2014, 35(2): 153-162.

Wang Wenqiang, Sun Xiaoli. WEAK CONVERGENCE AND WEAK STABILITY OF IMPLICIT EULER METHOD FOR STOCHASTIC FRACTIONAL DIFFERENTIAL EQUATION[J]. Journal of Numerical Methods and Computer Applications, 2014, 35(2): 153-162.

WEAK CONVERGENCE AND WEAK STABILITY OF IMPLICIT EULER METHOD FOR STOCHASTIC FRACTIONAL DIFFERENTIAL EQUATION

Wang Wenqiang, Sun Xiaoli   

  1. School of Mathematics and Computational Science, Xiangtan University, Xiangtan 411105, Hunan, China
  • Received:2013-12-23 Online:2014-06-15 Published:2014-05-29
本文主要研究了一类随机分数阶微分方程隐式Euler方法的弱收敛性与弱稳定性.首先构造了数值求解随机分数阶微分方程的隐式Euler方法,然后证明该方法是弱稳定的和1阶弱收敛的,文末给出的数值算例验证了所获得的理论结果的正确性.
The authors mainly study the weak convergence and weak stability of implicit Euler method for stochastic fractional differential equation. In this paper, an implicit numerical method for the stochastic fractional differential equation is proposed. 1-order weak convergence and weak stability of the implicit Euler method are established. Finally, one numerical example is given. The theoretical results are also confirmed by a numerical experiment.

MR(2010)主题分类: 

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[1] Anh V V, Mcvinish R. Fractional differential equations driven by Lévy noise[J]. Journal of Applied Mathematics and Stochastic Analysis, 2003, 16(2): 97-119.

[2] Latifa Debbia, Marco Dozzi. On the solutions of nonlinear stochastic fractional partial differential equations in one spatial dimension[J]. Stochastic Processes and their Applications, 2005, (115): 1764-1781.

[3] Jumarie G. Modeling fractional stochastic systems as non-random fractional dynamics driven by Brownian motions[J]. Applied Mathematical Modelling, 2008, 32(5): 836-859.

[4] Anh V V, Yong J M, Yu Z G. Stochastic modeling of the auroral electrojet index[J]. Journal of Geophysical Research, 2008, (113): 1-16.

[5] Yu Z G, Anh V V, Wang Y, Mao D, Wanliss J. Modeling and simulation of the horizontal component of the geomagnetic field by fractional stochastic differential equations in conjunction with empirical mode decomposition[J]. Journal of Geophysical Research, 2010, (115): 1-11.

[6] Shi K H, Wang Y J. On a stochastic fractional partial differential equation driven by a Lévy space-time white noise[J]. Journal of Mathematical Analysis and Applications, 2010, 364(1): 119-129.

[7] Wu Dongsheng. On the solution process for a stochastic fractional partial differential equation driven by space-time white noise[J]. Statistics and Probability Letters, 2011, (81): 1161-1172.

[8] Sakthivel R, Revathi P, Ren Yong. Existence of solutions for nonlinear fractional stochastic differential equations[J]. Nonlinear Analysis, 2013, (81): 70-86.

[9] Chang C C. Numerical solution of stochastic differential equations[D]. University of California, Berkeley: Ph.D. Dissertation, 1985.

[10] Lubich Ch. Discretized fractional calculus[J]. SIAM J. Math. Anal., 1986, 17(3): 704-716.

[11] Gradinaru M, Nourdin I. Milstein's type schemes for fractional SDEs[J]. Annales de I'Institut Henri Poincare(B), Probability and Statistics, 2009, 45(4): 1085-1098.

[12] Kuo Hui-Hsiung. Introduction to stochastic integration[M]. New York: Springer-Verlag, 2006.

[13] Mao Xuerong. Stochastic differential equations and their applications[M]. Chichester: Horwood, 2007.

[14] Jiang Rong. Several numerical method for solve fractional differential equation problem[D]. Xiangtan University: Master Thesis, 2008.[in Chinese]

[15] Mihai Gradinaru, Ivan Nourdin. Milstein's type schemes for fractional SDEs[J]. Annales de I'Institut Henri Poincare(B), Probability and Statistics, 2009, 45(4): 1085-1098.

[16] Weilbeer M. Efficient numerical methods for fractional differential equations and their analytical background[D]. Ph.D. Thesis, 2005.

[17] Pedjeu J C, Ladde G S. Stochastic fractional differential equations: Modeling, metheod and analysis[J]. Chaos, Solitons Fractals, 2012, 45(3): 279-293.

[18] Kloeden P, Platen E. Numerical solution of stochastic differential equations[M]. Springer Verlag, Berlin, 1992.
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