Hyperbolic Anderson equations with general time-independent Gaussian noise: Stratonovich regime
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866911796145684480 |
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| author | Chen, Xia Hu, Yaozhong |
| author_facet | Chen, Xia Hu, Yaozhong |
| contents | In this paper, we investigate the
hyperbolic Anderson equation
generated by a time-independent Gaussian noise
with two objectives: The solvability and intermittency.
First, we prove that Dalang's condition is necessary and sufficient
for existence of the solution. Second, we establish the
precise long time and high moment asymptotics for the solution under
the usual homogeneity assumption of the covariance of the Gaussian noise.
Our approach is fundamentally different from the ones existing in
literature.
The main contributions in our approach include the representation of Stratonovich
moment under Laplace transform via the moments of the Brownian motions in
Gaussian potentials
and some large deviation skills developed
in dealing effectively with the Stratonovich chaos expansion. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_08603 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Hyperbolic Anderson equations with general time-independent Gaussian noise: Stratonovich regime Chen, Xia Hu, Yaozhong Probability 60F10, 60H15, 60H40, 60J65, 81U10 In this paper, we investigate the hyperbolic Anderson equation generated by a time-independent Gaussian noise with two objectives: The solvability and intermittency. First, we prove that Dalang's condition is necessary and sufficient for existence of the solution. Second, we establish the precise long time and high moment asymptotics for the solution under the usual homogeneity assumption of the covariance of the Gaussian noise. Our approach is fundamentally different from the ones existing in literature. The main contributions in our approach include the representation of Stratonovich moment under Laplace transform via the moments of the Brownian motions in Gaussian potentials and some large deviation skills developed in dealing effectively with the Stratonovich chaos expansion. |
| title | Hyperbolic Anderson equations with general time-independent Gaussian noise: Stratonovich regime |
| topic | Probability 60F10, 60H15, 60H40, 60J65, 81U10 |
| url | https://arxiv.org/abs/2403.08603 |