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Analysis and balance survey of discrete input‐output systems under random environment
Author(s) -
Geng XianMin,
Li Liang,
Geng YuChao,
Cao RongMei
Publication year - 2018
Publication title -
expert systems
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.365
H-Index - 38
eISSN - 1468-0394
pISSN - 0266-4720
DOI - 10.1111/j.1468-0394.2011.00592.x
Subject(s) - computer science , balance (ability) , eigenvalues and eigenvectors , markov chain , consumption (sociology) , matrix (chemical analysis) , discrete time and continuous time , mathematical optimization , mathematics , statistics , machine learning , medicine , social science , physics , materials science , quantum mechanics , sociology , composite material , physical medicine and rehabilitation
Under random environment, the balance survey is difficult in many fields, such as in the industrial structure, the economics, and the society. In this paper, we study the random dynamic input‐output model with consumption, in which the time‐delay is one; and analyze the existence of the balanced growth solution by the theory of Markov processes. We present a new criterion of the imbalanced survey, which is a positive right eigenvector of the expectation of a matrix associated with the input‐output model. We also will prove that the collapse time is finite almost surely, which indicates that the random dynamic input‐output model does not possess a balanced growth solution, and consequently, the economic system must be adjusted constantly.