The particle approximation of quasi-stationary distributions. Part~I: concentration bounds in the uniform case
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866909436184887296 |
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| author | Journel, Lucas Rousset, Mathias |
| author_facet | Journel, Lucas Rousset, Mathias |
| contents | We study mean-field particle approximations of normalized Feynman-Kac semi-groups, usually called Fleming-Viot or Feynman-Kac particle systems. Assuming various large time stability properties of the semi-group uniformly in the initial condition, we provide explicit time-uniform $L^p$ and exponential bounds (a new result) with the expected rate in terms of sample size. This work is based on a stochastic backward error analysis (similar to the classical concept of numerical analysis) of the measure-valued Markov particle estimator, an approach that simplifies methods previously used for time-uniform $L^p$ estimates. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_15820 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | The particle approximation of quasi-stationary distributions. Part~I: concentration bounds in the uniform case Journel, Lucas Rousset, Mathias Probability We study mean-field particle approximations of normalized Feynman-Kac semi-groups, usually called Fleming-Viot or Feynman-Kac particle systems. Assuming various large time stability properties of the semi-group uniformly in the initial condition, we provide explicit time-uniform $L^p$ and exponential bounds (a new result) with the expected rate in terms of sample size. This work is based on a stochastic backward error analysis (similar to the classical concept of numerical analysis) of the measure-valued Markov particle estimator, an approach that simplifies methods previously used for time-uniform $L^p$ estimates. |
| title | The particle approximation of quasi-stationary distributions. Part~I: concentration bounds in the uniform case |
| topic | Probability |
| url | https://arxiv.org/abs/2412.15820 |