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

## TL;DR

This paper establishes the strong convergence rate of the Euler-Maruyama method for stochastic differential equations with H"older continuous drift driven by symmetric $ ext{alpha}$-stable noise, revealing a rate of $peta/ ext{alpha}$ under certain conditions.

## Contribution

It provides a new convergence rate analysis for Euler-Maruyama applied to SDEs with H"older continuous drift and symmetric $ ext{alpha}$-stable noise, using novel proof techniques.

## Key findings

- Proves $L^p$ strong convergence rate of $peta/ ext{alpha}$.
- Extends understanding of numerical methods for SDEs with non-Lipschitz coefficients.
- Uses H"older's and Bihari's inequalities in the analysis.

## 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).