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

 آمار

تعداد نشریات43
تعداد شماره‌ها1,235
تعداد مقالات15,177
تعداد مشاهده مقاله50,684,773
تعداد دریافت فایل اصل مقاله13,769,863
Haghighi, Amir. (1402). A modi fied split-step truncated Euler-Maruyama method for SDEs with non-globally Lipschitz continuous coefficients. سامانه مدیریت نشریات علمی, 11(3), 522-534. doi: 10.22034/cmde.2022.52638.2212
Amir Haghighi. "A modi fied split-step truncated Euler-Maruyama method for SDEs with non-globally Lipschitz continuous coefficients". سامانه مدیریت نشریات علمی, 11, 3, 1402, 522-534. doi: 10.22034/cmde.2022.52638.2212
Haghighi, Amir. (1402). 'A modi fied split-step truncated Euler-Maruyama method for SDEs with non-globally Lipschitz continuous coefficients', سامانه مدیریت نشریات علمی, 11(3), pp. 522-534. doi: 10.22034/cmde.2022.52638.2212
Haghighi, Amir. A modi fied split-step truncated Euler-Maruyama method for SDEs with non-globally Lipschitz continuous coefficients. سامانه مدیریت نشریات علمی, 1402; 11(3): 522-534. doi: 10.22034/cmde.2022.52638.2212

A modi fied split-step truncated Euler-Maruyama method for SDEs with non-globally Lipschitz continuous coefficients

Computational Methods for Differential Equations
مقاله 6، دوره 11، شماره 3، شهریور 2023، صفحه 522-534    اصل مقاله (396.05 K)
نوع مقاله: Research Paper
شناسه دیجیتال (DOI): 10.22034/cmde.2022.52638.2212
نویسنده
Amir Haghighi*
Department of Mathematics, Faculty of Science, Razi University, Kermanshah 67149, Iran.
چکیده
In this paper, we propose an explicit diffuse the split-step truncated Euler-Maruyama (DSSTEM) method for stochastic differential equations with non-global Lipschitz coefficients. We investigate the strong convergence of the new method under local Lipschitz and Khasiminskii-type conditions. We show that the newly proposed method achieves a strong convergence rate arbitrarily close to half under some additional conditions. Finally, we illustrate the efficiency and performance of the proposed method with numerical results.
کلیدواژه‌ها
Local Lipschitz condition؛ Khasiminskii condition؛ Truncated method؛ Split-step method؛ Strong convergence
مراجع
  • [1] M. Avaji, A. Jodayree Akbarfam, and A. Haghighi, Stability analysis of high order RungeKutta methods for index 1 stochastic differential-algebraic equations with scalar noise, Appl. Math. Comput., 362 (2019), 124544.
  • [2] O. Farkhondeh Rouz and D. Ahmadian, Mean-square stability of a constructed Third-order stochastic Runge-Kutta schemes for general stochastic differential equations, Comput. Methods Differ. Equ., 10(3) (2022), 617-638.
  • [3] Q. Guo, W. Liu, X. Mao and R. Yue, The partially truncated EulerMaruyama method and its stability and bound- edness, Appl. Numer. Math., 115 (2017), 235-251.
  • [4] Q. Guo, W. Liu, X. Mao and R. Yue, The truncated Milstein method for stochastic differential equations with commutative noise , J. Comput. Appl. Math., 338 (2018), 298-310.
  • [5] A. Haghighi and A. Robler, Split-step double balanced approximation methods for stiff stochastic differential equa- tions, Int. J. Comput. Math., 96(5) (2019) 1030-1047.
  • [6] D. J. Higham, X. Mao and A.M. Stuart, Strong convergence of Euler-type methods for nonlinear  stochastic  differ-  ential equations, SIAM J. Numer. Anal., 40(3) (2002), 10411063.
  • [7] L. Hu, X. Li and X. Mao, Convergence rate and stability of the truncated EulerMaruyama method for stochastic differential equations, J. Comput. Appl. Math., 337 (2018), 274-289.
  • [8] M. Hutzenthaler, A. Jentzen and P.E. Kloeden, Strong and weak divergence in finite time of Eulers method for stochastic differential equations with non-globally Lipschitz continuous coefficients, Proc. R. Soc. Lond. Ser. A Math. Phys. Eng. Sci., 467 (2011), 15631576.
  • [9] M. Hutzenthaler, A. Jentzen, and P.E. Kloeden, Strong convergence of an explicit numerical method for SDEs with non-globally Lipschitz continuous coefficients, Ann. Appl. Probab., 22(2) (2012), 16111641.
  • [10] P. E. Kloeden and E. Platen, Numerical Solution of Stochastic Differential Equations, Springer, Berlin, 2007.
  • [11] X. Li and G. Yin, Explicit Milstein schemes with truncation for nonlinear stochastic differential equations: Con- vergence and its rate, J. Comput. Appl. Math., 347 (2020) 112771.
  • [12] W. Liu and X. Mao , Strong convergence of the stopped Euler-Maruyama method for nonlinear stochastic differ- ential equations, Appl. Math. Comput., 223 (2013), 389-400.
  • [13] X. Mao, Stochastic Differential Equations and Applications, Horwood, Chichester, 2007.
  • [14] X. Mao and L. Szpruch, Strong convergence and stability of implicit numerical methods for stochastic differential equations with non-globally Lipschitz continuous coefficients , J. Comput. Appl. Math., 238 (2013), 14-28.
  • [15] X. Mao, The truncated Euler-Maruyama method for stochastic differential equations , J. Comput. Appl. Math., 290 (2015), 370-384.
  • [16] X. Mao, Convergence rates of the truncated EulerMaruyama method for stochastic differential equations, J. Com- put. Appl. Math., 296 (2016), 362-375.
  • [17] G .N. Milstein, Numerical Integration of Stochastic Differential Equations, Kluwer, Dordrecht, 1995.
  • [18] G. N. Milstein and M. V. Tretyakov, Stochastic Numerics for Mathematical Physics, Springer, Berlin, 2004.
  • [19] P. Nabati, A simulation study of the COVID-19 pandemic based on the Ornstein-Uhlenbeck processes, Comput. Methods Differ. Equ., 10(3) (2021), 738-745.
  • [20] A.  R¨oßler,  Runge-Kutta  methods  for  the  strong  approximation  of  solutions  of  stochastic  differential  equations, SIAM J. Math. Anal., 48(3) (2010), 922-952.
  • [21] S. Sabanis, A note on tamed Euler approximations, Electron. Comm. Probab., 18 (2013), 1-10.
  • [22] M. Shahmoradi, D. Ahmadian and M. Ranjbar, Mean-square stability of 1.5 strong convergence orders of diago- nally drift RungeKutta methods for a class of stochastic differential equations, Comp. Appl. Math., 40(4) (2021), 1-17.
  • [23] T. Tian and K. Burrage, Implicit Taylor methods for stiff stochastic differential equations., Appl. Numer. Math., 38(1) (2001), 167185.
  • [24] P. Wang and Z. Liu, Split-step backward balanced Milstein methods for stiff stochastic systems, Appl. Numer. Math. 59 (2009), 1198-1213.
  • [25] P. Wang and Y. Li , Split-step forward methods for stochastic differential equations., J. Comput. Appl. Math., 233(10) (2010), 2641-2651.
آمار
تعداد مشاهده مقاله: 208
تعداد دریافت فایل اصل مقاله: 361


سامانه مدیریت نشریات علمی. قدرت گرفته از سیناوب