For the \(1+1\) dimensional damped stochastic Klein-Gordon equation driven by additive space-time white noise, we show that random singularities associated with the law of the iterated logarithm exist and propagate in the same way as the stochastic wave equation without damping. The proof can be reduced to the critically damped case, though many details of the proof still differ from the wave equation case. Our result provides evidence for possible connections to microlocal analysis, i.e., the exact regularity and singularities described in this paper should admit wavefront set type descriptions whose propagation is determined by the highest order terms of the linear operator.
