= Gaussian coordinates of deterministic orthonormal Wiener integrands
{c}
{title2=$\xi_n=\int g_n\,dW\quad\text{independent }N(0,1)$}
Deterministic Itô integrals are jointly centered Gaussian by approximation from step functions and the <Itô isometry>. Their covariance is the L2 inner product of their integrands. Orthonormal integrands therefore produce independent standard-normal coordinates, with independence of a countable family understood through all finite subfamilies.
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