Strong convergence rate of Euler-Maruyama method for stochastic differential equations with Hölder continuous drift coefficient driven by symmetric $α$-stable process
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arXiv
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| Format: | Preprint |
| Publié: |
2019
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| _version_ | 1866929641159131136 |
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| author | Liu, Wei |
| author_facet | Liu, Wei |
| contents | Euler-Maruyama method is studied to approximate stochastic differential equations driven by the symmetric $α$-stable additive noise with the $β$ Hölder continuous drift coefficient. When $α\in (1,2)$ and $β\in (0,α/2)$, for $p \in (0,2]$ the $L^p$ strong convergence rate is proved to be $pβ/α$. The proofs in this paper are extensively based on Hölder's and Bihari's inequalities, which is significantly different from those in Huang and Liao (2018). |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1901_08742 |
| institution | arXiv |
| publishDate | 2019 |
| record_format | arxiv |
| spellingShingle | Strong convergence rate of Euler-Maruyama method for stochastic differential equations with Hölder continuous drift coefficient driven by symmetric $α$-stable process Liu, Wei Numerical Analysis Probability 65C30 Euler-Maruyama method is studied to approximate stochastic differential equations driven by the symmetric $α$-stable additive noise with the $β$ Hölder continuous drift coefficient. When $α\in (1,2)$ and $β\in (0,α/2)$, for $p \in (0,2]$ the $L^p$ strong convergence rate is proved to be $pβ/α$. The proofs in this paper are extensively based on Hölder's and Bihari's inequalities, which is significantly different from those in Huang and Liao (2018). |
| title | Strong convergence rate of Euler-Maruyama method for stochastic differential equations with Hölder continuous drift coefficient driven by symmetric $α$-stable process |
| topic | Numerical Analysis Probability 65C30 |
| url | https://arxiv.org/abs/1901.08742 |