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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
2021-08-20T08:25:14Z
dc.date.available
2021-07-15T10:55:50Z
dc.date.available
2021-08-20T08:25:14Z
dc.date.issued
2021-02
dc.identifier.issn
1099-4300
dc.identifier.other
10.3390/e23020241
en_US
dc.identifier.uri
http://hdl.handle.net/20.500.11850/495225
dc.identifier.doi
10.3929/ethz-b-000495225
dc.description.abstract
The Sigma-Pi structure investigated in this work consists of the sum of products of an increasing number of identically distributed random variables. It appears in stochastic processes with random coefficients and also in models of growth of entities such as business firms and cities. We study the Sigma-Pi structure with Bernoulli random variables and find that its probability distribution is always bounded from below by a power-law function regardless of whether the random variables are mutually independent or duplicated. In particular, we investigate the case in which the asymptotic probability distribution has always upper and lower power-law bounds with the same tail-index, which depends on the parameters of the distribution of the random variables. We illustrate the Sigma-Pi structure in the context of a simple growth model with successively born entities growing according to a stochastic proportional growth law, taking both Bernoulli, confirming the theoretical results, and half-normal random variables, for which the numerical results can be rationalized using insights from the Bernoulli case. We analyze the interdependence among entities represented by the product terms within the Sigma-Pi structure, the possible presence of memory in growth factors, and the contribution of each product term to the whole Sigma-Pi structure. We highlight the influence of the degree of interdependence among entities in the number of terms that effectively contribute to the total sum of sizes, reaching the limiting case of a single term dominating extreme values of the Sigma-Pi structure when all entities grow independently.
en_US
dc.format
application/pdf
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
probability theory
en_US
dc.subject
power-law
en_US
dc.subject
stochastic processes
en_US
dc.subject
random multiplicative process
en_US
dc.subject
growth model
en_US
dc.title
Sigma-Pi Structure with Bernoulli Random Variables: Power-Law Bounds for Probability Distributions and Growth Models with Interdependent Entities
en_US
dc.type
Journal Article
dc.rights.license
Creative Commons Attribution 4.0 International
dc.date.published
2021-02-19
ethz.journal.title
Entropy
ethz.journal.volume
23
en_US
ethz.journal.issue
2
en_US
ethz.journal.abbreviated
Entropy
ethz.pages.start
241
en_US
ethz.size
18 p.
en_US
ethz.version.deposit
publishedVersion
en_US
ethz.identifier.wos
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 (emeritus) / Sornette, Didier (emeritus)
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 (emeritus) / Sornette, Didier (emeritus)
ethz.date.deposited
2021-07-15T10:56:35Z
ethz.source
WOS
ethz.eth
yes
en_US
ethz.availability
Open access
en_US
ethz.rosetta.installDate
2021-08-20T08:25:22Z
ethz.rosetta.lastUpdated
2022-03-29T11:16:07Z
ethz.rosetta.exportRequired
true
ethz.rosetta.versionExported
true
ethz.COinS
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