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An efficient weak Euler–Maruyama type approximation scheme of very high dimensional SDEs by orthogonal random variables

Author

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  • Akahori, Jirô
  • Kinuya, Masahiro
  • Sawai, Takashi
  • Yuasa, Tomooki

Abstract

We will introduce Euler–Maruyama approximations given by an orthogonal system in L2[0,1] for high dimensional SDEs, which could be finite dimensional approximations of SPDEs. In general, the higher the dimension is, the more one needs to generate uniform random numbers at every time step in numerical simulation. The schemes proposed in this paper, in contrast, can deal with this problem by generating very few uniform random numbers at every time step. The schemes save time in the simulation of very high dimensional SDEs. In particular, we conclude that an Euler–Maruyama approximation based on the Walsh system is efficient in high dimensions.

Suggested Citation

  • Akahori, Jirô & Kinuya, Masahiro & Sawai, Takashi & Yuasa, Tomooki, 2021. "An efficient weak Euler–Maruyama type approximation scheme of very high dimensional SDEs by orthogonal random variables," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 187(C), pages 540-565.
    • Handle: RePEc:eee:matcom:v:187:y:2021:i:c:p:540-565
    DOI: 10.1016/j.matcom.2021.03.010
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    References listed on IDEAS

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    1. Ogawa, Shigeyoshi, 1995. "Some problems in the simulation of nonlinear diffusion processes," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 38(1), pages 217-223.
    2. Harase, Shin, 2019. "Conversion of Mersenne Twister to double-precision floating-point numbers," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 161(C), pages 76-83.
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    Cited by:

    1. Tsubasa Nishimura & Kenji Yasutomi & Tomooki Yuasa, 2022. "Higher-Order Error Estimates of the Discrete-Time Clark–Ocone Formula," Journal of Theoretical Probability, Springer, vol. 35(4), pages 2518-2539, December.

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