= Gaussian white noise model
{c}
{title2=$dY=f\,dt+n^{-1/2}dW$}
Observe $Y(t)=\int_0^tf(s)\,ds+\sigma W(t)$ on $[0,1]$, where $f\in L^2[0,1]$ is an unknown deterministic drift and $W$ is standard <Brownian motion>. The observation against a deterministic test <function> is $Y(h)=\langle f,h\rangle+\sigma W(h)$, with <covariance> $\sigma^2\langle h,g\rangle$. <Gaussian white noise> is represented by an <isonormal Gaussian process> on test <functions> rather than a pointwise noise <function>. Taking $\sigma=n^{-1/2}$ is the usual statistical scaling.
Back to article page
