On a class of linear models. (English) Zbl 0733.60076
Summary: This paper is concerned with classification criteria, asymptotic behaviour, and stationarity of a non-Markovian model with linear transition rule, called a linear OM-chain. These problems are solved by making use of the structure of the stochastic matrix appearing in the definition of such a model. The model studied includes as special cases the Markovian model as well as the linear learning model, and has applications in psychological and biological research, in control theory, and in adaptation theory.
MSC:
| 60G99 | Stochastic processes |
| 60J10 | Markov chains (discrete-time Markov processes on discrete state spaces) |
| 60J20 | Applications of Markov chains and discrete-time Markov processes on general state spaces (social mobility, learning theory, industrial processes, etc.) |
| 15B51 | Stochastic matrices |
Keywords:
discrete parameter stochastic processes; random systems with complete connections; Markov chains; recurrence; transience; classification criteria; asymptotic behaviour; stationarity; non-Markovian model; linear transition rule; linear OM-chain; linear learning modelReferences:
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