Ornstein-Uhlenbeck Fokker-Planck: stationary Gaussian p_s(x) = sqrt(kappa/(pisigma^2))exp(-kappa x^2/sigma^2)

Layer 1 — Physicsin the self-organization subtree

Ornstein-Uhlenbeck Fokker-Planck framework. Setup: stochastic differential equation dx = -kappa x dt + sigma dW with kappa > 0 (linear drift toward 0) and white-noise Wiener process dW of intensity sigma. Ito's lemma maps the OU SDE to a…

Related concepts

Itô's lemma
Theorem: OU stationary Gaussian p_s has FP residual exactly 0 and integral-norm exactly 1

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