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The convergence of a numerical scheme for additive fractional stochastic delay equations with H>12

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  • Mahmoudi, Fatemeh
  • Tahmasebi, Mahdieh

Abstract

In this paper, we investigate the strong convergence of the exponential Euler method to stochastic delay differential equations with fractional Brownian motion (FSDDEs) of Hurst parameter H∈(12,1). We establish the strong convergence rate H of the method for FSDDEs to the exact solution. Also we justify our theoretical results with some numerical examples of these equations alongside insignificant step size.

Suggested Citation

  • Mahmoudi, Fatemeh & Tahmasebi, Mahdieh, 2022. "The convergence of a numerical scheme for additive fractional stochastic delay equations with H>12," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 191(C), pages 219-231.
    • Handle: RePEc:eee:matcom:v:191:y:2022:i:c:p:219-231
    DOI: 10.1016/j.matcom.2021.08.010
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    References listed on IDEAS

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    1. Chunmei Shi & Yu Xiao & Chiping Zhang, 2012. "The Convergence and MS Stability of Exponential Euler Method for Semilinear Stochastic Differential Equations," Abstract and Applied Analysis, John Wiley & Sons, vol. 2012(1).
    2. Chunmei Shi & Yu Xiao & Chiping Zhang, 2012. "The Convergence and MS Stability of Exponential Euler Method for Semilinear Stochastic Differential Equations," Abstract and Applied Analysis, Hindawi, vol. 2012, pages 1-19, September.
    3. Küchler, Uwe & Platen, Eckhard, 2000. "Strong discrete time approximation of stochastic differential equations with time delay," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 54(1), pages 189-205.
    4. Mémin, Jean & Mishura, Yulia & Valkeila, Esko, 2001. "Inequalities for the moments of Wiener integrals with respect to a fractional Brownian motion," Statistics & Probability Letters, Elsevier, vol. 51(2), pages 197-206, January.
    5. Bellen, Alfredo & Zennaro, Marino, 2013. "Numerical Methods for Delay Differential Equations," OUP Catalogue, Oxford University Press, number 9780199671373.
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