Covariance operator of a Gaussian measure
= Covariance operator of a Gaussian measure
The <covariance operator> $K$ of a <Gaussian measure> on a real <Hilbert space> satisfies $\langle Kh,g\rangle=\operatorname{Cov}(\langle U,h\rangle,\langle U,g\rangle)$. A positive <self-adjoint operator> is the <covariance> of a Hilbert-space-valued <Gaussian random variable> exactly when it is <trace-class>.