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

Arzu Ahmadova and Nazim I. Mahmudov

Mathematics and Computers in Simulation (MATCOM), 2021, vol. 190, issue C, 429-448

Abstract: 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.

Keywords: Fractional stochastic Langevin equation; Mittag-Leffler type function; Mild solution; Existence and uniqueness; Strong convergence; Euler–Maruyama scheme (search for similar items in EconPapers)
Date: 2021
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Persistent link: https://EconPapers.repec.org/RePEc:eee:matcom:v:190:y:2021:i:c:p:429-448

DOI: 10.1016/j.matcom.2021.05.037

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