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<p>In this paper, the explicit expression of the Onsager–Machlup action functional to degenerate stochastic differential equations driven by fractional Brownian motion is derived, provided that the diffusion coefficient and reference path satisfy some suitable conditions. Furthermore, fractional Euler–Lagrange equations for the Onsager–Machlup action functional are also obtained, and some examples are provided to illustrate our results.</p>

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The Onsager–Machlup Action Functional for Degenerate Stochastic Differential Equations Driven by Fractional Brownian Motion

  • 期刊论文

  • 发表日期：

    2025年11月19日

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  • Shanqi Liu,
  • Hongjun Gao

摘要

In this paper, the explicit expression of the Onsager–Machlup action functional to degenerate stochastic differential equations driven by fractional Brownian motion is derived, provided that the diffusion coefficient and reference path satisfy some suitable conditions. Furthermore, fractional Euler–Lagrange equations for the Onsager–Machlup action functional are also obtained, and some examples are provided to illustrate our results.