Central limit theorem and moderate deviation principle for the stochastic generalized Burgers-Huxley equation with multiplicative noise
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arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866913448652177408 |
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| author | Kumar, Vivek Kumar, Ankit Mohan, Manil T. |
| author_facet | Kumar, Vivek Kumar, Ankit Mohan, Manil T. |
| contents | In this work, we investigate the Central Limit Theorem (CLT) and Moderate Deviation Principle (MDP) for the stochastic generalized Burgers-Huxley (SGBH) equation with multiplicative Gaussian noise. The SGBH equation is a diffusion-convection-reaction type equation which consists a nonlinearity of polynomial order, and we take into account of an infinite-dimensional noise having a coefficient that has linear growth. We first prove the CLT which allows us to establish the convergence of the distribution of the solution to a re-scaled SGBH equation to a desired distribution function. Furthermore, we extend our asymptotic analysis by investigating the MDP for the SGBH equation. Using the weak convergence method, we establish the MDP and derive the corresponding rate function. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_19107 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Central limit theorem and moderate deviation principle for the stochastic generalized Burgers-Huxley equation with multiplicative noise Kumar, Vivek Kumar, Ankit Mohan, Manil T. Probability In this work, we investigate the Central Limit Theorem (CLT) and Moderate Deviation Principle (MDP) for the stochastic generalized Burgers-Huxley (SGBH) equation with multiplicative Gaussian noise. The SGBH equation is a diffusion-convection-reaction type equation which consists a nonlinearity of polynomial order, and we take into account of an infinite-dimensional noise having a coefficient that has linear growth. We first prove the CLT which allows us to establish the convergence of the distribution of the solution to a re-scaled SGBH equation to a desired distribution function. Furthermore, we extend our asymptotic analysis by investigating the MDP for the SGBH equation. Using the weak convergence method, we establish the MDP and derive the corresponding rate function. |
| title | Central limit theorem and moderate deviation principle for the stochastic generalized Burgers-Huxley equation with multiplicative noise |
| topic | Probability |
| url | https://arxiv.org/abs/2407.19107 |