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

Wei Liu

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arXiv · 1901.08742

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

Wei Liu

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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).

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BibTeX RIS

Wei Liu. 2019-01-25. Strong convergence rate of Euler-Maruyama method for stochastic differential equations with H\"older continuous drift coefficient driven by symmetric $\alpha$-stable process. https://arxiv.org/abs/1901.08742

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