Matrix-noise Jacobians in stochastic-calculus inference and optimal paths (opens in new tab)

Multiplicative noise makes stochastic dynamics depend on how the white-noise limit is interpreted. In multidimensional systems with matrix-valued noise amplitudes $\sigma(x)$, this dependence includes a local Jacobian contribution that is absent from the scalar examples most often used to build intuition. We formulate a finite-step path-likelihood framework for $\theta$-discretized diffusions and show that its short-time expansion isolates the s...