Weak Error Estimates of Ergodic Approximations for Monotone Jump-diffusion SODEs
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866914541272563712 |
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| author | Liu, Zhihui Wu, Xiaoming |
| author_facet | Liu, Zhihui Wu, Xiaoming |
| contents | We first derive the exponential ergodicity of the stochastic theta method (STM) with $θ\in (1/2,1]$ for monotone jump-diffusion stochastic ordinary differential equations (SODEs) under a dissipative condition. Then we establish the weak error estimates of the backward Euler method (BEM), corresponding to the STM with $θ=1$. In particular, the time-independent estimate for the BEM in the jump-free case yields a one-order convergence rate between the exact and numerical invariant measures, answering a question left in {\it Z. Liu and Z. Liu, J. Sci. Comput. (2025) 103:87}. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_15698 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Weak Error Estimates of Ergodic Approximations for Monotone Jump-diffusion SODEs Liu, Zhihui Wu, Xiaoming Numerical Analysis Probability 60H35, 37M25, 65C30 We first derive the exponential ergodicity of the stochastic theta method (STM) with $θ\in (1/2,1]$ for monotone jump-diffusion stochastic ordinary differential equations (SODEs) under a dissipative condition. Then we establish the weak error estimates of the backward Euler method (BEM), corresponding to the STM with $θ=1$. In particular, the time-independent estimate for the BEM in the jump-free case yields a one-order convergence rate between the exact and numerical invariant measures, answering a question left in {\it Z. Liu and Z. Liu, J. Sci. Comput. (2025) 103:87}. |
| title | Weak Error Estimates of Ergodic Approximations for Monotone Jump-diffusion SODEs |
| topic | Numerical Analysis Probability 60H35, 37M25, 65C30 |
| url | https://arxiv.org/abs/2509.15698 |