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| Main Author: | |
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| Format: | Preprint |
| Published: |
2023
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2307.10889 |
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| _version_ | 1866916240896819200 |
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| author | Parekh, Shalin |
| author_facet | Parekh, Shalin |
| contents | A result of Arcones implies that if a measure-preserving linear operator $S$ on an abstract Wiener space $(X,H,μ)$ is strongly mixing, then the set of limit points of the random sequence $((2\log n)^{-1/2}S^n(x))_{n\in\mathbb N}$ equals the unit ball of $H$ for a.e. $x \in X$, which may be seen as a generalization of the classical Strassen's law of the iterated logarithm. We extend this result to the case of a continuous parameter $n$ and higher Gaussian chaoses, and we also prove a contraction-type principle for Strassen laws of such chaoses. We then use these extensions to recover or prove Strassen-type laws for a broad collection of processes derived from a Gaussian measure, including "nonlinear" Strassen laws for singular SPDEs such as the KPZ equation. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2307_10889 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | A nonlinear Strassen law for singular SPDEs Parekh, Shalin Probability Functional Analysis A result of Arcones implies that if a measure-preserving linear operator $S$ on an abstract Wiener space $(X,H,μ)$ is strongly mixing, then the set of limit points of the random sequence $((2\log n)^{-1/2}S^n(x))_{n\in\mathbb N}$ equals the unit ball of $H$ for a.e. $x \in X$, which may be seen as a generalization of the classical Strassen's law of the iterated logarithm. We extend this result to the case of a continuous parameter $n$ and higher Gaussian chaoses, and we also prove a contraction-type principle for Strassen laws of such chaoses. We then use these extensions to recover or prove Strassen-type laws for a broad collection of processes derived from a Gaussian measure, including "nonlinear" Strassen laws for singular SPDEs such as the KPZ equation. |
| title | A nonlinear Strassen law for singular SPDEs |
| topic | Probability Functional Analysis |
| url | https://arxiv.org/abs/2307.10889 |