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Convergence of the Euler-Maruyama method for stochastic differential equations driven by $G$-Brownian motion

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In this paper, we deal with the Euler-Maruyama (EM) \linebreak scheme for stochastic differential equations driven by $G$-Brownian motion ($G$-SDEs). Under the linear growth and the local Lipschitz conditions, the strong convergence as well as the rate of convergence of the EM numerical solution to the exact solution for $G$-SDEs are established.

Abstract

In this paper, we deal with the Euler-Maruyama (EM) \linebreak scheme for stochastic differential equations driven by $G$-Brownian motion ($G$-SDEs). Under the linear growth and the local Lipschitz conditions, the strong convergence as well as the rate of convergence of the EM numerical solution to the exact solution for $G$-SDEs are established.

참고문헌 (27)

  1. X. Bai, "On the existence and uniqueness of solutions to stochastic differential equations driven by G-Brownian motion with integral-Lipschitz coefficients", Acta Math. Appl. Sin. Engl. Ser, 30(3), pp.589~610 (2014)[DOI]
  2. J. Bao, "Approximations of McKean-Vlasov stochastic differential equations with irregular coefficients", J. Theoret. Probab, 35(2), pp.1187~1215 (2022)[DOI]
  3. J. Bao, "Convergence rate of Euler-Maruyama scheme for SDEs with H¨older-Dini continuous drifts", J. Theoret. Probab, 32(2), pp.848~871 (2019)[DOI]
  4. J. Bao, "Convergence rate of EM scheme for SDDEs", Proc. Amer. Math. Soc, 141(9), pp.3231~3243 (2013)[DOI]
  5. S. Deng, "Stability equivalence between the stochastic differential delay equations driven by G-Brownian motion and the Euler-Maruyama method", Appl. Math. Lett, 96, pp.138~146 (2019)[DOI]
  6. L. Denis, "Function spaces and capacity related to a sublinear expectation : Application to G-Brownian motion paths", Potential Anal, 34(2), pp.139~161 (2011)[DOI]
  7. F. Gao, "Pathwise properties and homeomorphic flows for stochastic differential equations driven by G-Brownian motion", Stochastic Process. Appl, 119(10), pp.3356~3382 (2009)[DOI]
  8. D. J. Higham, "Strong convergence of Euler-type methods for nonlinear stochastic differential equations", SIAM J. Numer. Anal, 40(3), pp.1041~1063 (2002)[DOI]
  9. M. Hu, "On representation theorem of G-expectations and paths of GBrownian motion", Acta Math. Appl. Sin. Engl. Ser, 25(3), pp.539~546 (2009)[DOI]
  10. M. Hutzenthaler, "Strong convergence of an explicit numerical method for SDEs with nonglobally Lipschitz continuous coefficients", Ann. Appl. Probab, 22(4), pp.1611~1641 (2012)[DOI]
  11. P. E. Kloeden, "Numerical solution of stochastic differential equations" (1992), Springer
  12. X. Li, "Lyapunov-type conditions and stochastic differential equations driven by G-Brownian motion", J. Math. Anal. Appl, 439(1), pp.235~255 (2016)[DOI]
  13. X. Li, "Explicit numerical approximations for stochastic differential equations in finite and infinite horizons: truncation methods, convergence in pth moment and stability", IMA J. Numer. Anal, 39(2), pp.847~892 (2019)[DOI]
  14. X. Li, "Stopping times and related Itˆo’s calculus with G-Brownian motion", Stochastic Process. Appl, 121(7), pp.1492~1508 (2011)[DOI]
  15. G. Li, "Convergence and asymptotical stability of numerical solutions for neutral stochastic delay differential equations driven by G-Brownian motion", Comput. Appl. Math, 37(4), pp.4301~4320 (2018)[DOI]
  16. X. Mao, "Stochastic Differential Equations and Their Applications" (1997), Horwood Publishing Series in Mathematics & Applications
  17. X. Mao, "The truncated Euler-Maruyama method for stochastic differential equations", J. Comput. Appl. Math, 290, pp.370~384 (2015)[DOI]
  18. S. Peng, "G-expectation, G-Brownian motion and related stochastic calculus of Ito type, in Stochastic analysis and applications", Abel Symp., pp.541~567 (2007)
  19. S. Peng, "Multi-dimensional G-Brownian motion and related stochastic calculus under G-expectation", Stochastic Process. Appl, 118(12), pp.2223~2253 (2008)[DOI]
  20. S. Peng, "Nonlinear expectations and stochastic calculus under uncertainty" (2019), Springer
  21. H. M. Soner, "Martingale representation theorem for the Gexpectation", Stochastic Process. Appl, 121(2), pp.265~287 (2011)[DOI]
  22. Y. Song, "Some properties on G-evaluation and its applications to G-martingale decomposition", Sci. China Math, 54(2), pp.287~300 (2011)[DOI]
  23. Y. Song, "Uniqueness of the representation for G-martingales with finite variation", Electron. J. Probab, 17(24), pp.15~ (2012)[DOI]
  24. R. Ullah, "On existence and approximate solutions for stochastic differential equations in the framework of G-Brownian motion", Eur. Phys. J. Plus, 132, pp.435~ (2017)[DOI]
  25. H. Wu, "Stability of numerical solution to pantograph stochastic functional differential equations", Appl. Math. Comput, 431, pp.127326~ (2022)[DOI]
  26. J. Yang, "Numerical simulations for G-Brownian motion", Front. Math. China, 11(6), pp.1625~1643 (2016)[DOI]
  27. C. Yuan, "A note on the rate of convergence of the Euler-Maruyama method for stochastic differential equations", Stoch. Anal. Appl, 26(2), pp.325~333 (2008)[DOI]

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