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arXiv · 2602.20836

Onsager--Machlup Functional for Fractional Stochastic Newton Dynamics with Time-Dependent Noise Intensities

Yanbin Zhu·Xiaomeng Jiang·Yong Li
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Abstract

In this paper, we derive the Onsager--Machlup functional for a second-order Newton-type stochastic system driven by time-dependent fractional noise, \[ X_t'' = f_t(X_t, X_t') + \sigma_t \,\xi_t^{H}, \] 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.

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Yanbin Zhu, Xiaomeng Jiang, Yong Li. 2026-02-24. Onsager--Machlup Functional for Fractional Stochastic Newton Dynamics with Time-Dependent Noise Intensities. https://arxiv.org/abs/2602.20836

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