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