The Onsager-Machlup action functional for degenerate SDEs driven by fractional Brownian motion

Shanqi Liu; Hongjun Gao

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arXiv · 2312.03269

The Onsager-Machlup action functional for degenerate SDEs driven by fractional Brownian motion

Shanqi Liu·Hongjun Gao

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Abstract

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

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Shanqi Liu, Hongjun Gao. 2023-12-06. The Onsager-Machlup action functional for degenerate SDEs driven by fractional Brownian motion. https://arxiv.org/abs/2312.03269

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