The Onsager-Machlup Action Functional for Degenerate McKean-Vlasov Stochastic Differential Equations
Hongjun Gao, Shanqi Liu
2024, v.30, Issue 3, 399-426
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.
doi:10.61102/1024-2953-mprf.2024.30.3.002
Keywords: Onsager-Machlup action functional; degenerate stochastic differential equations; McKean-Vlasov; Girsanov transformation
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