Diffusion amplitude ($d{X}_t=b(t,X_t)dt+\sigma (t,X_t)d{W}_t$)

The coefficient $\sigma$ multiplying the Brownian motion increment in a scalar stochastic differential equation. The local variance rate is ${\sigma }^2$, and the second-order coefficient in the backward Kolmogorov backward equation is ${\sigma }^2/2$. This distinguishes the amplitude from the physical diffusion coefficient convention $D={\sigma }^2/2$.