دانشگاه تبریز
فهرست نشریات دارای اعتبار وزارت علوم، تحقیقات و فناوری
پایگاه استنادی علوم جهان اسلام (ISC)

 آمار

تعداد نشریات45
تعداد شماره‌ها1,477
تعداد مقالات18,019
تعداد مشاهده مقاله58,375,976
تعداد دریافت فایل اصل مقاله19,804,227
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.
آمار
تعداد مشاهده مقاله: 863
تعداد دریافت فایل اصل مقاله: 912


سامانه مدیریت نشریات علمی. قدرت گرفته از سیناوب