caa a22 4500 605508186 CHVBK 20210128100635.0 cr unu---uuuuu 210128e20151201xx s 000 0 eng 10.1007/s00010-014-0318-y doi (NATIONALLICENCE)springer-10.1007/s00010-014-0318-y Dilatively stable stochastic processes and aggregate similarity [Elektronische Daten] [Mátyás Barczy, Peter Kern, Gyula Pap] Dilatively stable processes generalize the class of infinitely divisible self-similar processes. We reformulate and extend the definition of dilative stability introduced by Iglói (Dilative stability, Ph.D. Thesis, University of Debrecen, Faculty of Informatics, http://www.inf.unideb.hu/valseg/dolgozok/igloi/dissertation.pdf (2008)) using characteristic functions. We also generalize the concept of aggregate similarity introduced by Kaj (Fractals in Engineering, New Trends in Theory and Applications, pp 199-218 (2005)). It turns out that these two notions are essentially the same for infinitely divisible processes. Examples of dilatively stable generalized fractional Lévy processes are given and we point out that certain limit processes in aggregation models are dilatively stable. Springer Basel, 2014 Dilatively stable process nationallicence Self-similar process nationallicence Fractional Lévy motion nationallicence Aggregate similarity nationallicence Barczy Mátyás Faculty of Informatics, University of Debrecen, P.O. Box 12, 4010, Debrecen, Hungary aut Kern Peter Mathematical Institute, Heinrich-Heine-University Düsseldorf, Universitätsstr. 1, 40225, Düsseldorf, Germany aut Pap Gyula Bolyai Institute, University of Szeged, Aradi vértanúk tere 1, 6720, Szeged, Hungary aut Aequationes mathematicae Springer International Publishing 89/6(2015-12-01), 1485-1507 0001-9054 89:6<1485 2015 89 10 https://doi.org/10.1007/s00010-014-0318-y text/html Onlinezugriff via DOI BK010053 XK010053 XK010000 Metadata rights reserved Springer special CC-BY-NC licence nationallicence 1 research-article jats NATIONALLICENCE NATIONALLICENCE NL-springer NATIONALLICENCE 856 40 https://doi.org/10.1007/s00010-014-0318-y text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Barczy Mátyás Faculty of Informatics, University of Debrecen, P.O. Box 12, 4010, Debrecen, Hungary aut NATIONALLICENCE 700 1- Kern Peter Mathematical Institute, Heinrich-Heine-University Düsseldorf, Universitätsstr. 1, 40225, Düsseldorf, Germany aut NATIONALLICENCE 700 1- Pap Gyula Bolyai Institute, University of Szeged, Aradi vértanúk tere 1, 6720, Szeged, Hungary aut NATIONALLICENCE 773 0- Aequationes mathematicae Springer International Publishing 89/6(2015-12-01), 1485-1507 0001-9054 89:6<1485 2015 89 10