Strong rate of convergence for the Euler-Maruyama approximation of SDEs with H\"older continuous drift coefficient

By Olivier Menoukeu Pamen, Daichi Taguchi. 2015

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In this paper, we consider a numerical approximation of the stochastic differential equation (SDE) $$X_{t}=x_{0}+ \int_{0}^{t} b(s, X_{s}) \mathrm{d}s + L_{t},~x_{0} \in \mathbb{R}^{d},~t \in [0,T],$$ where the drift coefficient $b:[0,T] \times \mathbb{R}^d \to \mathbb{R}^d$ is H\"older continuous in both time and space variables and the noise $L=(L_t)_{0 \leq t \leq T}$ is a $d$-dimensional L\'evy process. We provide the rate of convergence for the Euler-Maruyama approximation when $L$ is a Wiener process or a truncated symmetric $\alpha$-stable process with $\alpha \in (1,2)$. Our technique is based on the regularity of the solution to the associated Kolmogorov equation.

Subfields: Demography, Finance

View Paper: https://www.semanticscholar.org/paper/dfcb11dac46e5a25e80d2c15b6175db7d6660569