  The current paper is devoted to the investigation of wave propagation
phenomenon in reaction-diffusion equations with ignition type nonlinearity in
time heterogeneous and random media. It is proven that such equations in time
heterogeneous media admit transition fronts or generalized traveling wave
solutions with time dependent profiles and that such equations in time random
media admit generalized traveling wave solutions with random profiles.
Important properties of generalized traveling wave solutions, including the
boundedness of propagation speeds and the uniform decaying estimates of the
propagation fronts, are also obtained.
