[en] The value of luminosity, synchrotron light source brightness, quantum lifetime, etc., for an electron storage ring is directly dependent upon the natural beam size and shape in the transverse phase space. These transverse beam parameters can be determined from the stationary particle distribution. A straightforward method was used to find the stationary distribution by solving the Fokker--Planck equation. From the expressions obtained invariant conditions between some of the beam parameters can easily be shown. These results were used to estimate the effects in PEP and SPEAR due to magnet alignment and vertical closed-orbit errors