English

Dilatively stable stochastic processes and aggregate similarity

Probability 2016-07-25 v3 Classical Analysis and ODEs

Abstract

Dilatively stable processes generalize the class of infinitely divisible self-similar processes. We reformulate and extend the definition of dilative stability introduced by Igl\'oi (2008) using characteristic functions. We also generalize the concept of aggregate similarity introduced by Kaj (2005). It turns out that these two notions are essentially the same for infinitely divisible processes. Examples of dilatively stable generalized fractional L\'evy processes are given and we point out that certain limit processes in aggregation models are dilatively stable.

Keywords

Cite

@article{arxiv.1408.3919,
  title  = {Dilatively stable stochastic processes and aggregate similarity},
  author = {Matyas Barczy and Peter Kern and Gyula Pap},
  journal= {arXiv preprint arXiv:1408.3919},
  year   = {2016}
}

Comments

21 pages. Title has been changed, and a new section on examples from aggregation models has been added

R2 v1 2026-06-22T05:31:43.739Z