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rareflow (version 0.1.0)

Freidlin_Wentzell_action: Freidlin-Wentzell Action Functional

Description

Computes the discrete Freidlin-Wentzell action for a path \(\phi(t)\) represented as a matrix of size \(T \times d\). The continuous action is:

Usage

Freidlin_Wentzell_action(phi, drift, dt)

Value

Numeric action value.

Arguments

phi

Matrix of path values of dimension \(T \times d\).

drift

Drift function \(b(x)\) returning a numeric vector.

dt

Time step.

Details

$$ I[\phi] = \frac{1}{2} \int_0^T \lVert \dot{\phi}(t) - b(\phi(t)) \rVert^2 \, dt $$

and the discrete approximation is:

$$ I \approx \frac{1}{2} \sum_{t=1}^{T-1} \lVert (\phi_{t+1} - \phi_t)/dt - b(\phi_t) \rVert^2 \, dt $$