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Recent developments in nonlinear stochastic modelling of social processes
Author(s) -
Bartholomew D. J.
Publication year - 1984
Publication title -
canadian journal of statistics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.804
H-Index - 51
eISSN - 1708-945X
pISSN - 0319-5724
DOI - 10.2307/3314723
Subject(s) - nonlinear system , markov chain , stochastic modelling , computer science , stochastic process , markov process , statistical physics , mathematics , mathematical optimization , econometrics , mathematical economics , statistics , machine learning , physics , quantum mechanics
After a brief review of social applications of Markov chains, the paper discusses nonlinear (“interactive”) Markov models in discrete and continuous time. The rather subtle relationship between the deterministic and stochastic versions of such models is explored by means of examples. It is shown that the behaviour of nonlinear systems over time periods of practical interest depends critically on the total size as well as on the system parameters. Particular attention is paid to strong and weak forms of quasi‐stationarity exhibited by stochastic systems.