Filtering and Statistical Properties of Unimodal Maps Perturbed by Heteroscedastic Noises
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| Main Authors: | , , , |
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| Format: | Preprint |
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2024
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| _version_ | 1866913584390340608 |
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| author | Lillo, Fabrizio Marmi, Stefano Tanzi, Matteo Vaienti, Sandro |
| author_facet | Lillo, Fabrizio Marmi, Stefano Tanzi, Matteo Vaienti, Sandro |
| contents | We propose a theory of unimodal maps perturbed by an heteroscedastic Markov chain noise and experiencing another heteroscedastic noise due to uncertain observation. We address and treat the filtering problem showing that by collecting more and more observations, one would predict the same distribution for the state of the underlying Markov chain no matter one's initial guess. Moreover we give other limit theorems, emphasizing in particular concentration inequalities and extreme value and Poisson distributions. Our results apply to a family of maps arising from a model of systemic risk in finance. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_13939 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Filtering and Statistical Properties of Unimodal Maps Perturbed by Heteroscedastic Noises Lillo, Fabrizio Marmi, Stefano Tanzi, Matteo Vaienti, Sandro Statistics Theory Dynamical Systems Probability We propose a theory of unimodal maps perturbed by an heteroscedastic Markov chain noise and experiencing another heteroscedastic noise due to uncertain observation. We address and treat the filtering problem showing that by collecting more and more observations, one would predict the same distribution for the state of the underlying Markov chain no matter one's initial guess. Moreover we give other limit theorems, emphasizing in particular concentration inequalities and extreme value and Poisson distributions. Our results apply to a family of maps arising from a model of systemic risk in finance. |
| title | Filtering and Statistical Properties of Unimodal Maps Perturbed by Heteroscedastic Noises |
| topic | Statistics Theory Dynamical Systems Probability |
| url | https://arxiv.org/abs/2411.13939 |