Convergence of the Euler-Maruyama method for multidimensional SDEs with discontinuous drift and degenerate diffusion coefficient

Gunther Leobacher; Michaela Szölgyenyi

doi:10.1007/s00211-017-0903-9

Convergence of the Euler-Maruyama method for multidimensional SDEs with discontinuous drift and degenerate diffusion coefficient

Gunther Leobacher
, Michaela Szölgyenyi

Institute for Statistics and Mathematics

Publication: Scientific journal › Journal article › peer-review

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Abstract

We prove strong convergence of order 1/4−ϵ for arbitrarily small ϵ>0 of the Euler–Maruyama method for multidimensional stochastic differential equations (SDEs) with discontinuous drift and degenerate diffusion coefficient. The proof is based on estimating the difference between the Euler–Maruyama scheme and another numerical method, which is constructed by applying the Euler–Maruyama scheme to a transformation of the SDE we aim to solve.

Original language	English
Pages (from-to)	219 - 239
Journal	Numerische Mathematik
Volume	138
Issue number	1
DOIs	https://doi.org/10.1007/s00211-017-0903-9
Publication status	Published - 2018

Austrian Classification of Fields of Science and Technology (ÖFOS)

101014 Numerical mathematics
401117 Viticulture
101024 Probability theory
101007 Financial mathematics

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title = "Convergence of the Euler-Maruyama method for multidimensional SDEs with discontinuous drift and degenerate diffusion coefficient",

abstract = "We prove strong convergence of order 1/4−ϵ for arbitrarily small ϵ>0 of the Euler–Maruyama method for multidimensional stochastic differential equations (SDEs) with discontinuous drift and degenerate diffusion coefficient. The proof is based on estimating the difference between the Euler–Maruyama scheme and another numerical method, which is constructed by applying the Euler–Maruyama scheme to a transformation of the SDE we aim to solve.",

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T1 - Convergence of the Euler-Maruyama method for multidimensional SDEs with discontinuous drift and degenerate diffusion coefficient

AU - Leobacher, Gunther

AU - Szölgyenyi, Michaela

PY - 2018

Y1 - 2018

N2 - We prove strong convergence of order 1/4−ϵ for arbitrarily small ϵ>0 of the Euler–Maruyama method for multidimensional stochastic differential equations (SDEs) with discontinuous drift and degenerate diffusion coefficient. The proof is based on estimating the difference between the Euler–Maruyama scheme and another numerical method, which is constructed by applying the Euler–Maruyama scheme to a transformation of the SDE we aim to solve.

AB - We prove strong convergence of order 1/4−ϵ for arbitrarily small ϵ>0 of the Euler–Maruyama method for multidimensional stochastic differential equations (SDEs) with discontinuous drift and degenerate diffusion coefficient. The proof is based on estimating the difference between the Euler–Maruyama scheme and another numerical method, which is constructed by applying the Euler–Maruyama scheme to a transformation of the SDE we aim to solve.

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Convergence of the Euler-Maruyama method for multidimensional SDEs with discontinuous drift and degenerate diffusion coefficient

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Austrian Classification of Fields of Science and Technology (ÖFOS)

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