Time-dependency in hyperbolic Anderson model: Stratonovich regime
Fuente:
arXiv
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| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866918152959426560 |
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| author | Chen, Xia |
| author_facet | Chen, Xia |
| contents | In this paper, the hyperbolic Anderson equation generated by a time-dependent Gaussian noise is under investigation in two fronts: The solvability and large-$t$ asymptotics. The investigation leads to a necessary and sufficient condition for existence and a precise large-$t$ limit form for the expectation of the solution. Three major developments are made for achieving these goals: A universal bound for Stratonovich moment that guarantees the Stratonovich integrability and ${\cal L}^2$-convergence of the Stratonovich chaos expansion under the best possible condition, a representation of the expected Stratonovich moments in terms of a time-randomized Brownian intersection local time, and a large deviation principle for the time-randomized Brownian intersection local time. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_01412 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Time-dependency in hyperbolic Anderson model: Stratonovich regime Chen, Xia Probability In this paper, the hyperbolic Anderson equation generated by a time-dependent Gaussian noise is under investigation in two fronts: The solvability and large-$t$ asymptotics. The investigation leads to a necessary and sufficient condition for existence and a precise large-$t$ limit form for the expectation of the solution. Three major developments are made for achieving these goals: A universal bound for Stratonovich moment that guarantees the Stratonovich integrability and ${\cal L}^2$-convergence of the Stratonovich chaos expansion under the best possible condition, a representation of the expected Stratonovich moments in terms of a time-randomized Brownian intersection local time, and a large deviation principle for the time-randomized Brownian intersection local time. |
| title | Time-dependency in hyperbolic Anderson model: Stratonovich regime |
| topic | Probability |
| url | https://arxiv.org/abs/2510.01412 |