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dc.contributor.author
De Sousa, Arthur M.Y.R.
dc.contributor.author
Takayasu, Hideki
dc.contributor.author
Sornette, Didier
dc.contributor.author
Takayasu, Misako
dc.date.accessioned
2017-11-28T07:40:10Z
dc.date.available
2017-11-22T07:40:59Z
dc.date.available
2017-11-27T10:04:09Z
dc.date.available
2017-10-06T02:55:40Z
dc.date.available
2017-10-17T09:09:57Z
dc.date.available
2017-10-26T15:56:58Z
dc.date.available
2017-11-27T10:05:21Z
dc.date.available
2017-11-28T07:40:10Z
dc.date.issued
2017-08
dc.identifier.issn
1099-4300
dc.identifier.other
10.3390/e19080417
en_US
dc.identifier.uri
http://hdl.handle.net/20.500.11850/214303
dc.identifier.doi
10.3929/ethz-b-000191179
dc.description.abstract
We introduce a simple growth model in which the sizes of entities evolve as multiplicative random processes that start at different times. A novel aspect we examine is the dependence among entities. For this, we consider three classes of dependence between growth factors governing the evolution of sizes: independence, Kesten dependence and mixed dependence. We take the sum X of the sizes of the entities as the representative quantity of the system, which has the structure of a sum of product terms (Sigma-Pi), whose asymptotic distribution function has a power-law tail behavior. We present evidence that the dependence type does not alter the asymptotic power-law tail behavior, nor the value of the tail exponent. However, the structure of the large values of the sum X is found to vary with the dependence between the growth factors (and thus the entities). In particular, for the independence case, we find that the large values of X are contributed by a single maximum size entity: the asymptotic power-law tail is the result of such single contribution to the sum, with this maximum contributing entity changing stochastically with time and with realizations.
en_US
dc.language.iso
en
en_US
dc.publisher
MDPI
en_US
dc.rights.uri
http://creativecommons.org/licenses/by/4.0/
dc.subject
Power-law
en_US
dc.subject
random multiplicative process
en_US
dc.subject
Stochastic process
en_US
dc.subject
Growth model
en_US
dc.subject
Dependence
en_US
dc.title
Power-Law Distributions from Sigma-Pi Structure of Sums of Random Multiplicative Processes
en_US
dc.type
Journal Article
dc.rights.license
Creative Commons Attribution 4.0 International
dc.date.published
2017-08-17
ethz.journal.title
Entropy
ethz.journal.volume
19
en_US
ethz.journal.issue
8
en_US
ethz.journal.abbreviated
Entropy
ethz.pages.start
417
en_US
ethz.size
13 p.
en_US
ethz.version.deposit
publishedVersion
en_US
ethz.identifier.wos
ethz.identifier.scopus
ethz.publication.place
Basel
en_US
ethz.publication.status
published
en_US
ethz.leitzahl
ETH Zürich::00002 - ETH Zürich::00012 - Lehre und Forschung::00007 - Departemente::02120 - Dep. Management, Technologie und Ökon. / Dep. of Management, Technology, and Ec.::03738 - Sornette, Didier / Sornette, Didier
en_US
ethz.leitzahl.certified
ETH Zürich::00002 - ETH Zürich::00012 - Lehre und Forschung::00007 - Departemente::02120 - Dep. Management, Technologie und Ökon. / Dep. of Management, Technology, and Ec.::03738 - Sornette, Didier / Sornette, Didier
en_US
ethz.leitzahl.certified
ETH Zürich::00002 - ETH Zürich::00012 - Lehre und Forschung::00007 - Departemente::02120 - Dep. Management, Technologie und Ökon. / Dep. of Management, Technology, and Ec.::03738 - Sornette, Didier / Sornette, Didier
en_US
ethz.date.deposited
2017-10-06T02:55:57Z
ethz.source
FORM
ethz.source
WOS
ethz.eth
yes
en_US
ethz.availability
Open access
en_US
ethz.rosetta.installDate
2017-11-28T07:36:53Z
ethz.rosetta.lastUpdated
2018-12-02T08:22:44Z
ethz.rosetta.exportRequired
true
ethz.rosetta.versionExported
true
dc.identifier.olduri
http://hdl.handle.net/20.500.11850/191179
dc.identifier.olduri
http://hdl.handle.net/20.500.11850/211816
ethz.COinS
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