= Continuous-time Gaussian white noise
{title2=$\langle A_i(t)A_j(s)\rangle=q\delta_{ij}\delta(t-s)$}
Continuous-time <Gaussian white noise> is a random distribution rather than an ordinary finite-variance function at every time. Integrating it against deterministic kernels gives <Gaussian random variables> with covariance $q\int f(s)g(s)ds$. For independent isotropic components, a three-dimensional dot covariance has amplitude $3q$. An ordinary rapidly decaying force covariance approximates this model only above its correlation time.
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