= First Gaussian chaos
{title2=$\mathcal G=\overline{\{\ell(X):\ell\in B^*\}}^{L^2}$}
For a centered <Gaussian random variable in a Banach space>, its first Gaussian chaos is the closed <linear subspace> of <L2 space> generated by its continuous linear observations. Every element is a centered <Gaussian random variable>, and every finite collection has a <multivariate normal distribution>: approximate in <L2 space> and pass to the <characteristic function>. The first Gaussian chaos supplies the scalar coordinates of its <Cameron-Martin space of a Gaussian random variable in a Banach space>.
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