Limiting behavior of inertial manifolds for stochastic differential equations driven by non-Gaussian Levy noise
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866911283254657024 |
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| author | Wu, Longyu Shu, Ji |
| author_facet | Wu, Longyu Shu, Ji |
| contents | In this paper, we study the limiting behavior for stochastic differential equations driven by non-Gaussian alpha-stable Levy noise as alpha approaches 2. We first prove the convergence of solutions for system driven by alpha-stable Levy noise to those of the system driven by Brownian motion. Then we construct the C^1 inertial manifolds for both systems and show that these inertial manifolds converge in probability as alpha rightarrow2. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_18461 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Limiting behavior of inertial manifolds for stochastic differential equations driven by non-Gaussian Levy noise Wu, Longyu Shu, Ji Dynamical Systems Probability In this paper, we study the limiting behavior for stochastic differential equations driven by non-Gaussian alpha-stable Levy noise as alpha approaches 2. We first prove the convergence of solutions for system driven by alpha-stable Levy noise to those of the system driven by Brownian motion. Then we construct the C^1 inertial manifolds for both systems and show that these inertial manifolds converge in probability as alpha rightarrow2. |
| title | Limiting behavior of inertial manifolds for stochastic differential equations driven by non-Gaussian Levy noise |
| topic | Dynamical Systems Probability |
| url | https://arxiv.org/abs/2511.18461 |