Stark broadening of atomic lines in plasmas is calculated by modelling the plasma stochastic electric field using the CTRW approach [1,2]. This allows retaining non Markovian terms in the Schrödinger equation averaged over the electric field
fluctuations. As an application we consider a special case of a non separable CTRW process, the so called Kangaroo process . An analytic expression for the line profile is presented for arbitrary waiting time distribution functions. A preliminary application to the hydrogen Lyman α line is discussed.