Computes the discrete Freidlin–Wentzell action for a path \(\phi(t)\)
represented as a matrix of size T × d. The continuous action is:
Usage
Freidlin_Wentzell_action(phi, drift, dt)
Arguments
- phi
Matrix of path values (T × d).
- drift
Drift function \(b(x)\) returning a numeric vector.
- dt
Time step.
Value
Numeric action value.
Details
$$
I[\phi] = \frac{1}{2} \int_0^T \| \dot{\phi}(t) - b(\phi(t)) \|^2 dt,
$$
and the discrete approximation is:
$$
I \approx \frac{1}{2} \sum_{t=1}^{T-1}
\| (\phi_{t+1} - \phi_t)/dt - b(\phi_t) \|^2 \, dt.
$$