Large Deviations for Iterated Sums and Integrals
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866914443391139840 |
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| author | Kifer, Yuri Zeitouni, Ofer |
| author_facet | Kifer, Yuri Zeitouni, Ofer |
| contents | We describe large deviations for normalized multiple iterated sums and integrals of the form $\bbS_N^{(ν)}(t)=N^{-ν}\sum_{0\leq k_1<...<k_ν\leq Nt}ξ(k_1)\otimes\cdots\otimesξ(k_ν)$, $t\in[0,T]$ and $\bbS_N^{(ν)}(t)=N^{-ν}\int_{0\leq s_1\leq...\leq s_ν\leq Nt}ξ(s_1)\otimes\cdots\otimesξ(s_ν)ds_1\cdots ds_ν$, where $\{ξ(k)\}_{-\infty<k<\infty}$ and $\{ξ(s)\}_{-\infty<s<\infty}$ are centered bounded stationary vector processes whose sums or integrals satisfy a trajectorial large deviations principle. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_09321 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Large Deviations for Iterated Sums and Integrals Kifer, Yuri Zeitouni, Ofer Probability 60F10 We describe large deviations for normalized multiple iterated sums and integrals of the form $\bbS_N^{(ν)}(t)=N^{-ν}\sum_{0\leq k_1<...<k_ν\leq Nt}ξ(k_1)\otimes\cdots\otimesξ(k_ν)$, $t\in[0,T]$ and $\bbS_N^{(ν)}(t)=N^{-ν}\int_{0\leq s_1\leq...\leq s_ν\leq Nt}ξ(s_1)\otimes\cdots\otimesξ(s_ν)ds_1\cdots ds_ν$, where $\{ξ(k)\}_{-\infty<k<\infty}$ and $\{ξ(s)\}_{-\infty<s<\infty}$ are centered bounded stationary vector processes whose sums or integrals satisfy a trajectorial large deviations principle. |
| title | Large Deviations for Iterated Sums and Integrals |
| topic | Probability 60F10 |
| url | https://arxiv.org/abs/2507.09321 |