On a discrete approximation of a skew stable Lévy process

Iksanov and Pilipenko (2023) defined a skew stable Lévy process as a scaling limit of a sequence of perturbed at $0$ symmetric stable Lévy processes (continuous-time processes). Here, we provide a simpler construction of the skew stable Lévy process as a scaling limit of a sequence of perturbed at $0$ standard random walks (random sequences).