  We develop a set of kinetic equations for hydrodynamic fluctuations which are
equivalent to nonlinear hydrodynamics with noise. The hydro-kinetic equations
can be coupled to existing second order hydrodynamic codes to incorporate the
physics of these fluctuations, which become dominant near the critical point.
We use the hydro-kinetic equations to calculate the modifications of energy
momentum tensor by thermal fluctuations from the earliest moments and at late
times in Bjorken expansion. The solution to the kinetic equations precisely
determines the coefficient of the first fractional power ($\propto
\tau^{-3/2}$) in the energy momentum tensor gradient expansion. Numerically, we
find that the contribution to the longitudinal pressure from hydrodynamic
fluctuations is comparable to the second order hydrodynamic terms for typical
medium parameters used to simulate heavy ion collisions.
