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

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}) $d$ s

L_{t},~x_{0} \in $R$ ^{d},~t \in [0,T],$ $w h e r e t h e d r i f t c o e f f i c i e n t$ b:[0,T] \times $R$ ^d \to $R$ ^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 $α$ -stable process with $α \in (1, 2)$ . Our technique is based on the regularity of the solution to the associated Kolmogorov equation.

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}) $d$ s

L_{t},~x_{0} \in $R$ ^{d},~t \in [0,T],$ $w h e r e t h e d r i f t c o e f f i c i e n t$ b:[0,T] \times $R$ ^d \to $R$ ^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 $α$ -stable process with $α \in (1, 2)$ . Our technique is based on the regularity of the solution to the associated Kolmogorov equation.

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