Multiplicative white noise can create new stable states absent in the deterministic system
Noise-induced transitions (Horsthemke & Lefever 1984): for SDE dx = f(x)dt + g(x)·σ dW, multiplicative noise g(x) ≠ const can qualitatively change the stationary distribution P(x) ∝ (g²)^(−1) exp(2∫f/g²). New peaks emerge at zeros of g(x)! A unimodal P (no noise) becomes bimodal above a critical σ². This is NOT the same as bistability — the deterministic system may have a single fixed point.