  Using the Langevin approach and the multiscale technique, a kinetic theory of
the time and space nonlocal fluctuations in the collisional plasma is
constructed. In local equilibrium a generalized version of the Callen-Welton
theorem is derived. It is shown that not only the dissipation but also the time
and space derivatives of the dispersion determine the amplitude and the width
of the spectrum lines of the electrostatic field fluctuations, as well as the
form factor. There appear significant differences with respect to the
non-uniform plasma. In the kinetic regime the form factor is more sensible to
space gradient than the spectral function of the electrostatic field
fluctuations. As a result of the inhomogeneity, these proprieties became
asymmetric with respect to the inversion of the frequency sign. The differences
in amplitude of peaks could become a new tool to diagnose slow time and space
variations in the plasma.

Plasma Physics