Tau energy losses at ultra-high energy: continuous versus stochastic treatment

We study the energy losses of the tau lepton in matter through electromagnetic processes at ultra-high energy (UHE). We use both a stochastic and a continuous framework to treat these interactions and compare the flux of tau leptons propagated after some amount of matter. We discuss the accuracy of the approximation of continuous energy losses by studying the propagation in standard rock of taus with both mono-energetic and power law injection spectra.