The work derives a unified approach to path measures via second-order HJ equations, showing equivalence of large deviation rate functions to Onsager-Machlup functionals and decomposing entropy production as the difference between forward and backward HJ equations.
Nualart.The Malliavin Calculus and Related Topics, volume 1995
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A study of path measures based on second-order Hamilton--Jacobi equations and their applications in stochastic thermodynamics
The work derives a unified approach to path measures via second-order HJ equations, showing equivalence of large deviation rate functions to Onsager-Machlup functionals and decomposing entropy production as the difference between forward and backward HJ equations.