On the Euler-Maruyama approximation for one-dimensional stochastic differential equations with irregular coefficients

By Hoang-Long Ngo, Daichi Taguchi. 2015

59 citations recorded by the source corpus.

We study the strong rates of the Euler-Maruyama approximation for one dimensional stochastic differential equations whose drift coefficient may be neither continuous nor one-sided Lipschitz and diffusion coefficient is Holder continuous. Especially, we show that the strong rate of the Euler-Maruyama approximation is 1/2 for a large class of equations whose drift is not continuous. We also provide the strong rate for equations whose drift is Holder continuous and diffusion is nonconstant

Subfields: Finance

View Paper: https://www.semanticscholar.org/paper/6b3ec153c06d7f39631205ecd33ed4cae467f268

How researchers see this paper

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In Finance

1. Hoang-Long Ngo
2. Daichi Taguchi
3. Andreas Neuenkirch
4. Michaela Szolgyenyi
5. Ivan Nourdin

Citations in the corpus

• The Euler–Maruyama scheme for SDEs with irregular drift: convergence rates via reduction to a quadrature problem (2019, result): “, by Ngo and Taguchi [22], and also the results of Pamen and Taguchi [25], Dareiotis and Gerencsér [2] rely on similar transformations.”
• Strong convergence for the Euler-Maruyama approximation of stochastic differential equations with discontinuous coefficients (2016, methodology): “The proof for the case b 6∈ L(1)(R) is based on the localisation technique given in [22] and it will be omitted.”