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arXiv · 2312.03472

The Onsager-Machlup action functional for degenerate McKean-Vlasov Stochastic Differential Equations

Shanqi Liu·Hongjun Gao
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Abstract

The purpose of this paper is to investigate the existence of the Onsager-Machlup action functional for degenerate McKean-Vlasov stochastic differential equations. To this end, we first derive Onsager-Machlup action functional for degenerate McKean-Vlasov stochastic differential equations with constant diffusion in a broad set of norms by Girsanov transformation, some conditioned exponential inequalities and It$\mathrm{\hat{o}}$ formulas for distribution dependent functional. Then an example is given to illustrate our results.

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Shanqi Liu, Hongjun Gao. 2023-12-06. The Onsager-Machlup action functional for degenerate McKean-Vlasov Stochastic Differential Equations. https://arxiv.org/abs/2312.03472

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