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Strong convergence rate of Euler-Maruyama method for stochastic differential equations with Hölder continuous drift coefficient driven by symmetric $α$-stable process (1901.08742v1)

Published 25 Jan 2019 in math.NA, cs.NA, and math.PR

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 $Lp$ 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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