  Systems living in complex non equilibrated environments often exhibit
subdiffusion characterized by a sublinear power-law scaling of the mean square
displacement. One of the most common models to describe such subdiffusive
dynamics is the continuous time random walk (CTRW). Stochastic trajectories of
a CTRW can be described mathematically in terms of a subordination of a normal
diffusive process by an inverse Levy-stable process. Here, we propose a simpler
Langevin formulation of CTRWs without subordination. By introducing a new type
of non-Gaussian noise, we are able to express the CTRW dynamics in terms of a
single Langevin equation in physical time with additive noise. We derive the
full multi-point statistics of this noise and compare it with the noise driving
scaled Brownian motion (SBM), an alternative stochastic model describing
subdiffusive behaviour. Interestingly, these two noises are identical up to the
level of the 2nd order correlation functions, but different in the higher order
statistics. We extend our formalism to general waiting time distributions and
force fields, and compare our results with those of SBM.
