Convergence rate of Euler-Maruyama scheme to the invariant probability measure under total variation distance
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866909935840788480 |
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| author | Wang, Yuke Ye, Yinna |
| author_facet | Wang, Yuke Ye, Yinna |
| contents | This article shows the geometric decay rate of Euler-Maruyama scheme for one-dimensional stochastic differential equation towards its invariant probability measure under total variation distance. Firstly, the existence and uniqueness of invariant probability measure and the uniform geometric ergodicity of the chain are studied through introduction of non-atomic Markov chains. Secondly, the equivalent conditions for uniform geometric ergodicity of the chain are discovered, by constructing a split Markov chain based on the original Euler-Maruyama scheme. It turns out that this convergence rate is independent with the step size under total variation distance. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2505_04218 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Convergence rate of Euler-Maruyama scheme to the invariant probability measure under total variation distance Wang, Yuke Ye, Yinna Probability Statistics Theory Primary 60J27, 60B10, 62E20, Secondary 60H10, 62L20, 37M25 This article shows the geometric decay rate of Euler-Maruyama scheme for one-dimensional stochastic differential equation towards its invariant probability measure under total variation distance. Firstly, the existence and uniqueness of invariant probability measure and the uniform geometric ergodicity of the chain are studied through introduction of non-atomic Markov chains. Secondly, the equivalent conditions for uniform geometric ergodicity of the chain are discovered, by constructing a split Markov chain based on the original Euler-Maruyama scheme. It turns out that this convergence rate is independent with the step size under total variation distance. |
| title | Convergence rate of Euler-Maruyama scheme to the invariant probability measure under total variation distance |
| topic | Probability Statistics Theory Primary 60J27, 60B10, 62E20, Secondary 60H10, 62L20, 37M25 |
| url | https://arxiv.org/abs/2505.04218 |