Linear Fractional Stable Motion with the rlfsm R Package

Linear fractional stable motion is a type of a stochastic integral driven by symmetric alpha-stable Lévy motion. The integral could be considered as a non-Gaussian analogue of the fractional Brownian motion. The present paper discusses R package rlfsm created for numerical procedures with the linear fractional stable motion. It is a set of tools for simulation of these processes as well as performing statistical inference and simulation studies on them. We introduce: tools that we developed to work with that type of motions as well as methods and ideas underlying them. Also we perform numerical experiments to show finite-sample behavior of certain estimators of the integral, and give an idea of how to envelope workflow related to the linear fractional stable motion in S4 classes and methods. Supplementary materials, including codes for numerical experiments, are available online. rlfsm could be found on CRAN and gitlab.

Stepan Mazur , Dmitry Otryakhin

Supplementary materials

Supplementary materials are available in addition to this article. It can be downloaded at

CRAN packages used

rlfsm, somebm, stabledist, stable, ggplot2

CRAN Task Views implied by cited packages

Distributions, Graphics, Phylogenetics, TeachingStatistics


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For attribution, please cite this work as

Mazur & Otryakhin, "The R Journal: Linear Fractional Stable Motion with the rlfsm R Package", The R Journal, 2020

BibTeX citation

  author = {Mazur, Stepan and Otryakhin, Dmitry},
  title = {The R Journal: Linear Fractional Stable Motion with the rlfsm R Package},
  journal = {The R Journal},
  year = {2020},
  note = {},
  doi = {10.32614/RJ-2020-008},
  volume = {12},
  issue = {1},
  issn = {2073-4859},
  pages = {386-405}