Euler-type approximation for the invariant measure: An abstract framework
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866910037383839744 |
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| author | Alfonsi, Aurélien Bally, Vlad Kohatsu-Higa, Arturo |
| author_facet | Alfonsi, Aurélien Bally, Vlad Kohatsu-Higa, Arturo |
| contents | We establish a general framework to study the rate of convergence of a Euler type approximation scheme with decreasing time steps to the invariant measure, for a general class of stochastic systems. The error is measured in general Wasserstein distances, which enables to encompass cases with non global contractivity conditions. Our main assumption is a coupling property which is expressed in terms of the one-step approximation. We show that the proposed set-up can be applied to a wide range of equations that may be law dependent, such as Langevin equations, reflected equations, Boltzmann type equations and for a recent McKean Vlasov type model for neuronal activity. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_03971 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Euler-type approximation for the invariant measure: An abstract framework Alfonsi, Aurélien Bally, Vlad Kohatsu-Higa, Arturo Probability 37M25, 60G99, 65C99 We establish a general framework to study the rate of convergence of a Euler type approximation scheme with decreasing time steps to the invariant measure, for a general class of stochastic systems. The error is measured in general Wasserstein distances, which enables to encompass cases with non global contractivity conditions. Our main assumption is a coupling property which is expressed in terms of the one-step approximation. We show that the proposed set-up can be applied to a wide range of equations that may be law dependent, such as Langevin equations, reflected equations, Boltzmann type equations and for a recent McKean Vlasov type model for neuronal activity. |
| title | Euler-type approximation for the invariant measure: An abstract framework |
| topic | Probability 37M25, 60G99, 65C99 |
| url | https://arxiv.org/abs/2509.03971 |