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

Shanqi Liu and Hongjun Gao ()
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Shanqi Liu: Great Bay University, Great Bay Institute for Advanced Study, School of Sciences
Hongjun Gao: Southeast University, School of Mathematics

Journal of Theoretical Probability, 2026, vol. 39, issue 1, 1-43

Abstract: Abstract 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.

Keywords: Onsager–Machlup action functional; Degenerate stochastic differential equations; Fractional Brownian motion; Primary 60H10; Secondary 60F99; 60G22; 82C35 (search for similar items in EconPapers)
Date: 2026
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DOI: 10.1007/s10959-025-01463-4

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