  We provide a closed-form autocorrelation function and power spectral density
(PSD) of the solution, along a prescribed probing direction, to a noisy version
of an optically pumped Bloch equation wherein each component of the external
magnetic field is subject to (possibly correlated) white noise. We conclude
that, up to first order in the white noise covariance amplitudes, noise in the
bias B-field direction does not affect the autocorrelation function. Moreover,
the noise terms for the remaining two axes make different contributions to the
magnetic noise-driven spin PSD; in particular, the contribution corresponding
to noises perpendicular to the probing direction dominates at high frequencies.
Some results concerning the second (and higher) order terms are given, and an
effective Larmor frequency shift caused by anisotropic transversal B-field
noises, towards the DC direction, is revealed. The analytic results are
supported by Monte Carlo simulations employing the Euler-Maruyama method.
