  We study the dynamics of fronts when both inertial effects and external
fluctuations are taken into account. Stochastic fluctuations are introduced as
multiplicative noise arising from a control parameter of the system. Contrary
to the non-inertial (overdamped) case, we find that important features of the
system, such as the velocity selection picture, are not modified by the noise.
We then compute the overdamped limit of the underdamped dynamics in a more
careful way, finding that it does not exhibit any effect of noise either. Our
result poses the question as to whether or not external noise sources can be
measured in physical systems of this kind.
