  We study the rapidity window dependences of higher order cumulants of
conserved charges observed in relativistic heavy ion collisions. The time
evolution and the rapidity window dependence of the non-Gaussian fluctuations
are described by the diffusion master equation. Analytic formulas for the time
evolution of cumulants in a rapidity window are obtained for arbitrary initial
conditions. We discuss that the rapidity window dependences of the non-Gaussian
cumulants have characteristic structures reflecting the non-equilibrium
property of fluctuations, which can be observed in relativistic heavy ion
collisions with the present detectors. It is argued that various information on
the thermal and transport properties of the hot medium can be revealed
experimentally by the study of the rapidity window dependences, especially by
the combined use, of the higher order cumulants. Formulas of higher order
cumulants for a probability distribution composed of sub-probabilities, which
are useful for various studies of non-Gaussian cumulants, are also presented.
