Time development of a Markov process in a finite population

Application to diffusion of information

Bibliographic Data

ID10142202
AuthorsKarmeshu Karmeshu (University of Waterloo, corresponding author), R K Pathria (University of Waterloo)
Year1980
Volume7
Issue2
Pages229-240
Publication date1980-11-01
Peer ReviewedYes
Open AccessNo
TypeARTICLE
VenueJournal of Mathematical Sociology (JOURNAL)
Journal identifiersISSN: 0022-250X • E-ISSN: 1545-5874
PublisherTaylor & Francis (PUBLISHER • GB)
DOI10.1080/0022250x.1980.9989909
OpenAlexW2012030585
LanguageEN
Citations received4
References cited5

A systematic procedure of truncating the hierarchy of moment equations describing the stochastic evolution of a Markov process in a finite population is developed. The procedure makes use of the asymptotic expression for a certain higher‐order moment of the relevant probability distribution and yields finite‐size corrections to all lower‐order moments. The usefulness of the method is illustrated by applying it to study the mean and the variance of the stochastic variable n(t), the number of active spreaders at time t, in Bartholomew's model of diffusion of information. The results thus obtained are compared with the ones following from the exact probability distribution for the model (wherever known) and the agreement between the two sets of results is found to be remarkably good

Diffusion · Hierarchy · Markov chain · Markov process · Mathematical optimization · Moment (physics · Physics · Population · Random variable · Statistical physics · Statistics · Variance (accounting · Applied Mathematics · Mathematics · Opinion Dynamics and Social Influence · Random Matrices and Applications · Stochastic processes and statistical mechanics

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