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

2023/12/06 by Shanqi Liu, Hui Gao, Liu, Shanqi +1
Economics, Econometrics and Finance · Engineering · Mathematics · #FOS: Mathematics #Nonlinear Partial Differential Equations #Probability (math.PR) #Stability and Controllability of Differential Equations #Stochastic processes and financial applications

paper · pdf · doi:10.48550/arxiv.2312.03472

openalex publication_date 2023/12/06 · openalex created_date 2023/12/08 · openalex updated_date 2026/07/28

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\mathrmo formulas for distribution dependent functional. Then an example is given to illustrate our results.

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