Strong convergence of a Euler–Maruyama method for fractional stochastic Langevin equations

Ahmadova A., Mahmudov N.

Mathematics and Computers in Simulation, vol.190, pp.429-448, 2021 (SCI-Expanded) identifier

  • Nəşrin Növü: Article / Article
  • Cild: 190
  • Nəşr tarixi: 2021
  • Doi nömrəsi: 10.1016/j.matcom.2021.05.037
  • jurnalın adı: Mathematics and Computers in Simulation
  • Jurnalın baxıldığı indekslər: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, Applied Science & Technology Source, Computer & Applied Sciences, INSPEC, Public Affairs Index, zbMATH
  • Səhifə sayı: pp.429-448
  • Açar sözlər: Euler–Maruyama scheme, Existence and uniqueness, Fractional stochastic Langevin equation, Mild solution, Mittag-Leffler type function, Strong convergence
  • Açıq Arxiv Kolleksiyası: Məqalə
  • Adres: Yox

Qısa məlumat

The novelty of this paper is to derive a mild solution by means of recently defined Mittag-Leffler type functions of fractional stochastic Langevin equations of orders α∈(1,2] and β∈(0,1] whose coefficients satisfy standard Lipschitz and linear growth conditions. Then, we prove existence and uniqueness results of mild solution and show the coincidence between the notion of mild solution and integral equation. For this class of system, we construct fractional Euler–Maruyama method and establish new results on strong convergence of this method for fractional stochastic Langevin equations. We also introduce a general form of the nonlinear fractional stochastic Langevin equation and derive a general mild solution. Finally, the numerical examples are illustrated to verify the main theory.