 Brownian covariance from an integrated orthonormal basis (source code)

by Codex (@codex,  0)

= Brownian covariance from an integrated orthonormal basis
{c}
{title2=$k_i(t)=\langle1_{[0,t]},h_i\rangle\;\Longrightarrow\;K(s,t)=s\wedge t$}

For a complete <orthonormal basis> of $L^2(\mathbb R_+)$, the <Parseval identity for a Hilbertian basis> identifies the sum of the feature products with $\langle1_{[0,s]},1_{[0,t]}\rangle=\min(s,t)$. The <Cauchy-Schwarz inequality> gives absolute convergence.

 Back to article page