On the Poisson equation for nonreversible Markov jump processes
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
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2023
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| _version_ | 1866909158589071360 |
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| author | Khodabandehlou, Faezeh Maes, Christian Netočný, Karel |
| author_facet | Khodabandehlou, Faezeh Maes, Christian Netočný, Karel |
| contents | We study the solution $V$ of the Poisson equation $LV + f=0$ where $L$ is the backward generator of an irreducible (finite) Markov jump process and $f$ is a given centered state function. Bounds on $V$ are obtained using a graphical representation derived from the Matrix Forest Theorem and using a relation with mean first-passage times. Applications include estimating time-accumulated differences during relaxation toward a steady nonequilibrium regime. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2310_19219 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | On the Poisson equation for nonreversible Markov jump processes Khodabandehlou, Faezeh Maes, Christian Netočný, Karel Probability Statistical Mechanics Mathematical Physics We study the solution $V$ of the Poisson equation $LV + f=0$ where $L$ is the backward generator of an irreducible (finite) Markov jump process and $f$ is a given centered state function. Bounds on $V$ are obtained using a graphical representation derived from the Matrix Forest Theorem and using a relation with mean first-passage times. Applications include estimating time-accumulated differences during relaxation toward a steady nonequilibrium regime. |
| title | On the Poisson equation for nonreversible Markov jump processes |
| topic | Probability Statistical Mechanics Mathematical Physics |
| url | https://arxiv.org/abs/2310.19219 |