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

Jiro Akahori, Masahiro Kinuya, Takashi Sawai and Tomooki Yuasa

Mathematics and Computers in Simulation (MATCOM), 2021, vol. 187, issue C, 540-565

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.

Keywords: Euler–Maruyama schemes; Stochastic differential equations; Monte Carlo method; High dimensional simulation; Weak rate of convergence; Itô–Taylor expansion; Wagner–Platen expansion (search for similar items in EconPapers)
Date: 2021
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:matcom:v:187:y:2021:i:c:p:540-565

DOI: 10.1016/j.matcom.2021.03.010

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