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فهرست نشریات دارای اعتبار وزارت علوم، تحقیقات و فناوری
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Mahmoudi, Fatemeh, Tahmasebi, Mahdieh. (1401). The convergence of exponential Euler method for weighted fractional stochastic equations. سامانه مدیریت نشریات علمی, 10(2), 538-548. doi: 10.22034/cmde.2021.41430.1795
Fatemeh Mahmoudi; Mahdieh Tahmasebi. "The convergence of exponential Euler method for weighted fractional stochastic equations". سامانه مدیریت نشریات علمی, 10, 2, 1401, 538-548. doi: 10.22034/cmde.2021.41430.1795
Mahmoudi, Fatemeh, Tahmasebi, Mahdieh. (1401). 'The convergence of exponential Euler method for weighted fractional stochastic equations', سامانه مدیریت نشریات علمی, 10(2), pp. 538-548. doi: 10.22034/cmde.2021.41430.1795
Mahmoudi, Fatemeh, Tahmasebi, Mahdieh. The convergence of exponential Euler method for weighted fractional stochastic equations. سامانه مدیریت نشریات علمی, 1401; 10(2): 538-548. doi: 10.22034/cmde.2021.41430.1795

The convergence of exponential Euler method for weighted fractional stochastic equations

Computational Methods for Differential Equations
مقاله 19، دوره 10، شماره 2، تیر 2022، صفحه 538-548    اصل مقاله (157.36 K)
نوع مقاله: Research Paper
شناسه دیجیتال (DOI): 10.22034/cmde.2021.41430.1795
نویسندگان
Fatemeh Mahmoudi1؛ Mahdieh Tahmasebi* 2
1Department of Mathematics, Karaj Branch, Islamic Azad University, Karaj, Iran.
2Department of Mathematical Sciences, Tarbiat Modares University, P.O. Box 14115-134, Tehran, Iran.
چکیده
‎In this paper‎, ‎we propose an exponential Euler method to approximate the solution of a stochastic functional differential equation driven by weighted fractional Brownian motion $ B^{ a‎, ‎b}$ under some assumptions on $a$ and $b$‎. ‎We obtain also the convergence rate of the method to the true solution after proving an $L^{ 2}$-maximal bound for the stochastic integrals in this case‎.
کلیدواژه‌ها
Malliavin calculus؛ Stochastic differential equations؛ Weighted fractional Brownian motion؛ Exponential Euler scheme
مراجع
  • [1]          AM. Abylayeva, R. Oinarov, and LE. Persson, Boundedness and compactness of a class of Hardy type operators, Luleå University of Technology, Graphic Production, 2016.
  • [2]          E. Alòs, O. Mazet, and D. Nualart, Stochastic calculus with respect to Gaussian processes, Ann Probab, 29 (2001), 766-801.
  • [3]          E. Alòs and D. Nualart, Stochastic calculus with respect to fractional Brownian motion, Stochastics and Stochastic Reports, 75(3), 129-152.
  • [4]          F. Biagini, Y. Hu, B. Øksendal, and T. Zhang, Stochastic Calculus for fBm and Applications, Probability and Its Application, Springer, Berlin, 2008.
  • [5]          P. Embrechts and M. Maejima, Self-Similar Processes, Wiley, NewYork, Princeton University Press, 2002.
  • [6]          T. Caraballo, M.J. Garrido-Atienza and T. Taniguchi,The existence and exponential behavior of solutions to stochastic delay evolution equations with a fractional Brownian motion, Nonlinear Analysis, 74 (2011), 3671– 3684.
  • [7]          S. Chunmei, Y. Xiao, and C. Zhang, The convergence and MS stability of Exponential Euler method for semilinear stochastic differential equations, Abstract and Applied Analysis, ID (2012), 350-407.
  • [8]          M. Gradinaru, I. Nourdin, F. Russo, and P.  Vallois, m-order integrals and generalized Itô’s formula; the case of  a fBm with any Hurst index, Ann. Inst. Henri Poincare ́ Probab. Stat, 41 (2005), 781-806.
  • [9]          Y. Hu, Integral transformations and anticipative calculus for fractional Brownian motions, Mem. Amer. Math. Soc., 175 (825), (2005).
  • [10]        M. Kamrani and N. Jamshidi, Implicit Euler approximation of stochastic evolution equations with fractional  Brownian motion, Communications in Nonlinear Science and Numerical Simulation, 44 (2017), 1-10.
  • [11]        YS. Mishura, Stochastic Calculus for Fractional Brownian Motion and Related Processes, Lect. Notes Math., Vol. 1929, Berlin, Heidelberg, Springer, 2008.
  • [12]        D. Nualart, Malliavin Calculus and Related Topics, 2nd ed., Springer, New York, 2006.
  • [13]        V. Pipiras and MS. Taqqu, Integration questions related to fractional Brownian motion, Probab. Theory Relat.  Fields, 118 (2000), 251-291.
  • [14]        G. Samorodnitsky, Long Range Dependence, Heavy Tails and Rare Events, Lecture Notes, MaPhySto, Centre for Mathematical Physics and Stochastics, Aarhus, 2002.
  • [15]        G. Samorodnitsky and MS. Taqqu, Stable Non-Gaussian Random Variables, Chapmanand Hall, London, 1994.
  • [16]        O. Sheluhin, S. Smolskiy, and A. Osin, Self-Similar Processes in Telecommunications, John Wiley Sons, Inc, New York, 2007.
  • [17]        GJ. Shen, XW. Yin, and LT. Yan, Least squares estimation for Ornstein-Uhlenbeck processes driven by the weighted fractional Brownian motion, Acta Math. Sci., 36 (2016), 394-408.
  • [18]        MS. Taqqu, A bibliographical guide to selfsimilar processes and long-range dependence, in Dependence in Probability and Statistics,(eds E. Eberlein and M.S. Taqqu), Birkhauser, Boston, (1986), 137-162.
  • [19]        W. Willinger, MS. Taqqu, and V. Teverovsky, Stock market prices and long-range dependence, Finance Stoch., 3(1) (1999), 1-13.
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