Local linearization for the nonlinear damped stochastic Klein-Gordon equation
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2026
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| Acceso en línea: | |
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| _version_ | 1866909987568091136 |
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| author | Rang, Guanglin Wang, Ran |
| author_facet | Rang, Guanglin Wang, Ran |
| contents | For the $1+1$ dimensional nonlinear damped stochastic Klein-Gordon equation driven by space-time white noise, we prove that the second-order increments of the solution can be approximated, after scaling with the diffusion coefficient, by those of the corresponding linearized stochastic Klein-Gordon equation. This extends the result of Huang et al. \cite{HOO2024} for the stochastic wave equation. A key difficulty arises from the more complex structure of the Green function, which we overcome by means of subtle analytical estimates. As applications, we analyze the quadratic variation of the solution and construct a consistent estimator for the diffusion parameter. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_07176 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Local linearization for the nonlinear damped stochastic Klein-Gordon equation Rang, Guanglin Wang, Ran Probability 60H15, 60G17, 60G22 For the $1+1$ dimensional nonlinear damped stochastic Klein-Gordon equation driven by space-time white noise, we prove that the second-order increments of the solution can be approximated, after scaling with the diffusion coefficient, by those of the corresponding linearized stochastic Klein-Gordon equation. This extends the result of Huang et al. \cite{HOO2024} for the stochastic wave equation. A key difficulty arises from the more complex structure of the Green function, which we overcome by means of subtle analytical estimates. As applications, we analyze the quadratic variation of the solution and construct a consistent estimator for the diffusion parameter. |
| title | Local linearization for the nonlinear damped stochastic Klein-Gordon equation |
| topic | Probability 60H15, 60G17, 60G22 |
| url | https://arxiv.org/abs/2601.07176 |