Strong convergence rate of Euler-Maruyama method for stochastic differential equations with H\"older continuous drift coefficient driven by symmetric $\alpha$-stable process

Abstract

Euler-Maruyama method is studied to approximate stochastic differential equations driven by the symmetric $\alpha$-stable additive noise with the $\beta$ H\"older continuous drift coefficient. When $\alpha \in (1,2)$ and $\beta \in (0,\alpha/2)$, for $p \in (0,2]$ the $L^p$ strong convergence rate is proved to be $p\beta/\alpha$. The proofs in this paper are extensively based on H\"older's and Bihari's inequalities, which is significantly different from those in Huang and Liao (2018).