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Relativistic dissipative hydrodynamics including hydrodynamic fluctuations isformulated by putting an emphasis on non-linearity and causality. As aconsequence of causality, dissipative currents become dynamical variables andnoises appeared in an integral form of constitutive equations should be coloredones from fluctuation-dissipation relations. Nevertheless noises turn out to bewhite ones in its differential form when noises are assumed to be Gaussian. Theobtained ifferential equations are very useful in numerical implementation ofrelativistic fluctuating hydrodynamics.

Relativistic fluctuating hydrodynamics with memory functions and colored noises