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Research Article

Truncated Euler–Maruyama method for stochastic differential equations driven by fractional Brownian motion with super-linear drift coefficient

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Pages 2184-2195 | Received 21 Jul 2022, Accepted 27 Sep 2023, Published online: 10 Oct 2023

References

  • F. Biagini, Y. Hu, B. Øksendal, and T. Zhang, Stochastic Calculus for Fractional Brownian Motion and Applications, Springer Science and Business Media, 2008.
  • A. Deya, A. Neuenkirch, and S. Tindel, A Milstein-type scheme without Lévy area terms for SDEs driven by fractional Brownian motion, in Ann. Inst. H. Poincaré Probab. Statist., Vol. 48, 2012, pp. 518–550.
  • T.E. Duncan, Y. Hu, and B. Pasik-Duncan, Stochastic calculus for fractional Brownian motion I. Theory, SIAM J. Control Optim. 38 (2000), pp. 582–612.
  • M.J. Garrido-Atienza, P.E. Kloeden, and A. Neuenkirch, Discretization of stationary solutions of stochastic systems driven by fractional Brownian motion, Appl. Math. Optim. 60 (2009), pp. 151–172.
  • 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), pp. 298–310.
  • Q. Guo, X. Mao, and R. Yue, The truncated Euler-Maruyama method for stochastic differential delay equations, Numer. Algorithms 78 (2018), pp. 599–624.
  • J. Hong, C. Huang, M. Kamrani, and X. Wang, Optimal strong convergence rate of a backward Euler type scheme for the Cox-Ingersoll-Ross model driven by fractional Brownian motion, Stoch. Process. Appl. 130 (2020), pp. 2675–2692.
  • L. Hu, X. Li, and X. Mao, Convergence rate and stability of the truncated Euler–Maruyama method for stochastic differential equations, J. Comput. Appl. Math. 337 (2018), pp. 274–289.
  • Y. Hu, D. Nualart, and X. Song, A singular stochastic differential equation driven by fractional Brownian motion, Statist. Probab. Lett. 78 (2008), pp. 2075–2085.
  • Y. Hu, Y. Liu, and D. Nualart, Rate of convergence and asymptotic error distribution of Euler approximation schemes for fractional diffusions, Ann. Appl. Probab. 26 (2016), pp. 1147–1207.
  • Y. Hu, Y. Liu, and D. Nualart, Crank-Nicolson scheme for stochastic differential equations driven by fractional Brownian motions, Ann. Appl. Probab. 31 (2021), pp. 39–83.
  • P.E. Kloeden, A. Neuenkirch, and R. Pavani, Multilevel Monte Carlo for stochastic differential equations with additive fractional noise, Ann. Oper. Res. 189 (2011), pp. 255–276.
  • M. Li, Y. Hu, C. Huang, and X. Wang, Mean square stability of stochastic theta method for stochastic differential equations driven by fractional Brownian motion, preprint (2021). Available at arXiv:2109.09009.
  • L. Lima, Fractional Brownian motion analysis for spreading of novel coronavirus, (1995). Available at SSRN 4019254.
  • X. Mao, The truncated Euler-Maruyama method for stochastic differential equations, J. Comput. Appl. Math. 290 (2015), pp. 370–384.
  • X. Mao, Convergence rates of the truncated Euler-Maruyama method for stochastic differential equations, J. Comput. Appl. Math. 296 (2016), pp. 362–375.
  • I.S. Mishura, I.U.S. Mishura, J.S. Mišura, Y. Mishura, and Û.S. Mišura, Stochastic Calculus for Fractional Brownian Motion and Related Processes, Vol. 1929, Springer Science and Business Media, 2008.
  • I. Norros, On the use of fractional Brownian motion in the theory of connectionless networks, IEEE J. Sel. Areas Commun. 13 (1995), pp. 953–962.
  • A. Stuart and A.R. Humphries, Dynamical Systems and Numerical Analysis, Vol. 2, Cambridge University Press, 1998.
  • M. Wang, X. Dai, and A. Xiao, Optimal convergence rate of B-Maruyama method for stochastic volterra integro-differential equations with Riemann-Liouville fractional Brownian motion, Adv. Appl. Math. Mech. 14 (2022), pp. 202–217.
  • L. Yan, W. Pei, and Z. Zhang, Exponential stability of sdes driven by fractional Brownian motion with markovian switching, Discrete Contin. Dyn. Syst. 39 (2019), pp. 6467–6483.
  • S. Zhang and C. Yuan, Stochastic differential equations driven by fractional Brownian motion with locally Lipschitz drift and their implicit Euler approximation, Proc. Roy. Soc. Edinburgh Sect. A 151 (2021), pp. 1278–1304.
  • H. Zhou, Y. Hu, and Y. Liu, Backward Euler method for stochastic differential equations with non-Lipschitz coefficients driven by fractional Brownian motion, BIT 63 (2023), pp. 40.

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