  We present stability estimates for the inverse source problem of the
stochastic Helmholtz equation in two and three dimensions by either near-field
or far-field data. The random source is assumed to be a microlocally isotropic
generalized Gaussian random function. For the direct problem, by exploring the
regularity of the Green function, we demonstrate that the direct problem admits
a unique bounded solution with an explicit integral representation, which
enhances the existing regularity result. For the case using near-field data,
the analysis of the inverse problem employs microlocal analysis to achieve an
estimate for the Fourier transform of the micro-correlation strength by the
near-field correlation data and a high-frequency tail. The stability follows by
showing the analyticity of the data and applying a novel analytic continuation
principle. The stability estimate by far-field data is derived by investigating
the correlation of the far-field data. The stability estimate consists of the
Lipschitz type data discrepancy and the logarithmic stability. The latter
decreases as the upper bound of the frequency increases, which exhibits the
phenomenon of increasing stability.
