Onsager–Machlup functional

The Onsager–Machlup functional is the action in the exponential of an additive Gaussian stochastic path probability. For $\dot{x}=b(x)+\sigma \Lambda$, its elementary discretization contains $\int |\dot{x}-b(x){|}^2/(2{\sigma }^2)dt$, with convention-dependent Jacobian terms for multiplicative or state-dependent drift.