Concentration bounds for stochastic systems with singular kernels
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866916274648383488 |
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| author | Jackson, Joe Zitridis, Antonios |
| author_facet | Jackson, Joe Zitridis, Antonios |
| contents | This note is concerned with weakly interacting stochastic particle systems with possibly singular pairwise interactions. In this setting, we observe a connection between entropic propagation of chaos and exponential concentration bounds for the empirical measure of the system. In particular, we establish a variational upper bound for the probability of a certain rare event, and then use this upper bound to show that "controlled" entropic propagation of chaos implies an exponential concentration bound for the empirical measure. This connection allows us to infer concentration bounds for a class of singular stochastic systems through a simple adaptation of the arguments developed in Jabin and Wang (2018). |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_02848 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Concentration bounds for stochastic systems with singular kernels Jackson, Joe Zitridis, Antonios Probability Mathematical Physics Analysis of PDEs This note is concerned with weakly interacting stochastic particle systems with possibly singular pairwise interactions. In this setting, we observe a connection between entropic propagation of chaos and exponential concentration bounds for the empirical measure of the system. In particular, we establish a variational upper bound for the probability of a certain rare event, and then use this upper bound to show that "controlled" entropic propagation of chaos implies an exponential concentration bound for the empirical measure. This connection allows us to infer concentration bounds for a class of singular stochastic systems through a simple adaptation of the arguments developed in Jabin and Wang (2018). |
| title | Concentration bounds for stochastic systems with singular kernels |
| topic | Probability Mathematical Physics Analysis of PDEs |
| url | https://arxiv.org/abs/2406.02848 |