  For thermally fluctuating 2-d systems, like solid surfaces, time and space
correlation of the local surface height diverge logarithmically in the rough
phase, whereas saturation is obtained below the roughening transition. A 2-d
Langevin formalism, allowing to recover for long times and/or large distances
these asymptotic behaviors, is presented. An overall expression for correlation
functions that are related to atom hopping rates and surface stiffnesses is
given. Considering anisotropic systems allows describing vicinal surfaces. At
finite times, time correlations cross over to power laws alpha*t^(1/n) (n = 1,
2 or 4), within limited time ranges as it was observed for isolated fluctuating
steps. Limits of time ranges are related to stiffnesses and diffusion
anisotropies. Application to the analysis of STM images of Cu(115) below the
roughening transition is given.
