On a discrete approximation of a skew stable L\'{e}vy process

Congzao Dong; Oleksandr Iksanov; Andrey Pilipenko

On a discrete approximation of a skew stable L\'{e}vy process

Probability 2023-07-12 v2

Authors: Congzao Dong , Oleksandr Iksanov , Andrey Pilipenko

Abstract

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

Keywords

lévy processes markov processes stochastic processes

Cite

@article{arxiv.2302.07298,
  title  = {On a discrete approximation of a skew stable L\'{e}vy process},
  author = {Congzao Dong and Oleksandr Iksanov and Andrey Pilipenko},
  journal= {arXiv preprint arXiv:2302.07298},
  year   = {2023}
}