Polynomial rates via deconvolution for nonparametric estimation in McKean-Vlasov SDEs
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arXiv
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| Autores principales: | , , , , |
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| Formato: | Preprint |
| Publicado: |
2024
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| Materias: | |
| Acceso en línea: | |
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| _version_ | 1866910678617423872 |
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| author | Amorino, Chiara Belomestny, Denis Pilipauskaitė, Vytautė Podolskij, Mark Zhou, Shi-Yuan |
| author_facet | Amorino, Chiara Belomestny, Denis Pilipauskaitė, Vytautė Podolskij, Mark Zhou, Shi-Yuan |
| contents | This paper investigates the estimation of the interaction function for a class of McKean-Vlasov stochastic differential equations. The estimation is based on observations of the associated particle system at time $T$, considering the scenario where both the time horizon $T$ and the number of particles $N$ tend to infinity. Our proposed method recovers polynomial rates of convergence for the resulting estimator. This is achieved under the assumption of exponentially decaying tails for the interaction function. Additionally, we conduct a thorough analysis of the transform of the associated invariant density as a complex function, providing essential insights for our main results. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_04667 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Polynomial rates via deconvolution for nonparametric estimation in McKean-Vlasov SDEs Amorino, Chiara Belomestny, Denis Pilipauskaitė, Vytautė Podolskij, Mark Zhou, Shi-Yuan Statistics Theory This paper investigates the estimation of the interaction function for a class of McKean-Vlasov stochastic differential equations. The estimation is based on observations of the associated particle system at time $T$, considering the scenario where both the time horizon $T$ and the number of particles $N$ tend to infinity. Our proposed method recovers polynomial rates of convergence for the resulting estimator. This is achieved under the assumption of exponentially decaying tails for the interaction function. Additionally, we conduct a thorough analysis of the transform of the associated invariant density as a complex function, providing essential insights for our main results. |
| title | Polynomial rates via deconvolution for nonparametric estimation in McKean-Vlasov SDEs |
| topic | Statistics Theory |
| url | https://arxiv.org/abs/2401.04667 |