Onsager--Machlup Functional for Fractional Stochastic Newton Dynamics with Time-Dependent Noise Intensities
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866917291524882432 |
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| author | Zhu, Yanbin Jiang, Xiaomeng Li, Yong |
| author_facet | Zhu, Yanbin Jiang, Xiaomeng Li, Yong |
| contents | In this paper, we derive the Onsager--Machlup functional for a second-order Newton-type stochastic system driven by time-dependent fractional noise, \[
X_t'' = f_t(X_t, X_t') + σ_t \,ξ_t^{H}, \] where \( H \in (1/4,1) \). The analysis relies on applying a Girsanov transformation to the non-degenerate components and evaluating the limiting conditional expectation associated with the noise term, for which the stochastic Fubini theorem plays a crucial role. To illustrate the applicability of the result, we study two mechanical systems perturbed by noise and provide supporting numerical simulations. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2602_20836 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Onsager--Machlup Functional for Fractional Stochastic Newton Dynamics with Time-Dependent Noise Intensities Zhu, Yanbin Jiang, Xiaomeng Li, Yong Dynamical Systems 60H10, 60G22, 60F10 In this paper, we derive the Onsager--Machlup functional for a second-order Newton-type stochastic system driven by time-dependent fractional noise, \[ X_t'' = f_t(X_t, X_t') + σ_t \,ξ_t^{H}, \] where \( H \in (1/4,1) \). The analysis relies on applying a Girsanov transformation to the non-degenerate components and evaluating the limiting conditional expectation associated with the noise term, for which the stochastic Fubini theorem plays a crucial role. To illustrate the applicability of the result, we study two mechanical systems perturbed by noise and provide supporting numerical simulations. |
| title | Onsager--Machlup Functional for Fractional Stochastic Newton Dynamics with Time-Dependent Noise Intensities |
| topic | Dynamical Systems 60H10, 60G22, 60F10 |
| url | https://arxiv.org/abs/2602.20836 |