Onsager-Machlup functional for stochastic lattice dynamical systems driven by time-varying noise
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866910567714783232 |
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| author | Zhang, Xinze Li, Yong |
| author_facet | Zhang, Xinze Li, Yong |
| contents | This paper investigates the Onsager-Machlup functional of stochastic lattice dynamical systems (SLDSs) driven by time-varying noise. We extend the Onsager-Machlup functional from finite-dimensional to infinite-dimensional systems, and from constant to time-varying diffusion coefficients. We first verify the existence and uniqueness of general SLDS solutions in the infinite sequence weighted space $l^2_ρ$. Building on this foundation, we employ techniques such as the infinite-dimensional Girsanov transform, Karhunen-Loève expansion, and probability estimation of Brownian motion balls to derive the Onsager-Machlup functionals for SLDSs in $l^2_ρ$ space. Additionally, we use a numerical example to illustrate our theoretical findings, based on the Euler Lagrange equation corresponding to the Onsage Machup functional. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_08465 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Onsager-Machlup functional for stochastic lattice dynamical systems driven by time-varying noise Zhang, Xinze Li, Yong Probability Classical Analysis and ODEs 82C35, 37L60, 60H15, 37H10 This paper investigates the Onsager-Machlup functional of stochastic lattice dynamical systems (SLDSs) driven by time-varying noise. We extend the Onsager-Machlup functional from finite-dimensional to infinite-dimensional systems, and from constant to time-varying diffusion coefficients. We first verify the existence and uniqueness of general SLDS solutions in the infinite sequence weighted space $l^2_ρ$. Building on this foundation, we employ techniques such as the infinite-dimensional Girsanov transform, Karhunen-Loève expansion, and probability estimation of Brownian motion balls to derive the Onsager-Machlup functionals for SLDSs in $l^2_ρ$ space. Additionally, we use a numerical example to illustrate our theoretical findings, based on the Euler Lagrange equation corresponding to the Onsage Machup functional. |
| title | Onsager-Machlup functional for stochastic lattice dynamical systems driven by time-varying noise |
| topic | Probability Classical Analysis and ODEs 82C35, 37L60, 60H15, 37H10 |
| url | https://arxiv.org/abs/2408.08465 |