  Relativistic dissipative hydrodynamics including hydrodynamic fluctuations is
formulated by putting an emphasis on non-linearity and causality. As a
consequence of causality, dissipative currents become dynamical variables and
noises appeared in an integral form of constitutive equations should be colored
ones from fluctuation-dissipation relations. Nevertheless noises turn out to be
white ones in its differential form when noises are assumed to be Gaussian. The
obtained ifferential equations are very useful in numerical implementation of
relativistic fluctuating hydrodynamics.
