Integrated square of Brownian motion
= Integrated square of Brownian motion
{title2=$Q=\int_0^1W_t^2\,dt$}
The quadratic functional $Q=\int_0^1W_t^2dt$ is finite almost surely. The <Brownian half-integer sine expansion> writes it as a sum of independent scaled squared standard normals. Its mean is $1/2$, and its Laplace transform is determined by a hyperbolic cosine product.