= Gaussian process construction from square-summable features
{c}
{title2=$X_t=\sum_i k_i(t)\xi_i,\quad K(s,t)=\sum_i k_i(s)k_i(t)$}
For independent standard normal variables $\xi_i$ and $\sum_i k_i(t)^2<\infty$ at each fixed time, the series defines $X_t$ in $L^2$. Every finite linear combination is an $L^2$ limit of Gaussian variables and is Gaussian. Thus this constructs a <Gaussian process> with the Gram <covariance kernel> $K$. It supplies no sample-path continuity without additional assumptions.
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