A kinetic description of Alfvén-cyclotron magnetic fluctuations for anisotropic electron-proton quasistable plasmas is studied. An analytical treatment, based on the fluctuation-dissipation theorem, consistently shows that spontaneous fluctuations in plasmas with stable distributions significantly contribute to the observed magnetic fluctuations in the solar wind, as seen, for example, in [S. D. Bale et al., Phys. Rev. Lett. 103, 211101 (2009)], even far below from the instability thresholds. Furthermore, these results, which do not require any adjustable parameters or wave excitations, are consistent with the results provided by hybrid simulations. It is expected that this analysis contributes to our understanding of the nature of magnetic fluctuations in the solar wind.