Dilatively stable stochastic processes and aggregate similarity

Barczy, Mátyás and Peter, Kern and Pap, Gyula (2015) Dilatively stable stochastic processes and aggregate similarity. AEQUATIONES MATHEMATICAE, 89 (6). pp. 1485-1507. ISSN 0001-9054

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Abstract

Dilatively stable processes generalize the class of infinitely divisible self-similar pro- cesses. We reformulate and extend the definition of dilative stability introduced by Igl´oi (2008) using characteristic functions. We also generalize the concept of aggregate similar- ity 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.

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