English

Continuous time random walk as a random walk in a random environment

Probability 2017-09-12 v2

Abstract

We show that for a weakly dense subset of the domain of attraction of a positive stable random variable of index 0<α<10<\alpha<1(DOA(α))DOA\left(\alpha\right)) the functional stable convergence is a time-changed renewal convergence of distribution of finite mean. Applied to Continuous Time Random Walk(CTRW) \'a la Montroll and Wiess we show that CTRW with renewal times in a weakly dense set of DOA(α)DOA\left(\alpha\right) can be realized as random walk in a random environment. We find the quenched limit and give a bound on the error of the approximation.

Keywords

Cite

@article{arxiv.1709.02141,
  title  = {Continuous time random walk as a random walk in a random environment},
  author = {Ofer Busani},
  journal= {arXiv preprint arXiv:1709.02141},
  year   = {2017}
}
R2 v1 2026-06-22T21:35:41.722Z