Asymptotic properties of recurrent random sequences

Author(s):  
Valery Buldygin ◽  
Serguei Solntsev

1980 ◽  
Vol 12 (4) ◽  
pp. 922-941
Author(s):  
Peter Findeisen

One general and three specialized models of the Bush–Mosteller type are presented to describe the kind of learning experiment where the response of the learner is always reinforced. Inhomogeneity is admitted. The random sequences of response probabilities and of responses associated with the different models are considered. Information about the existence and the distribution of asymptotic response probabilities is provided. The stress is on sufficient and necessary conditions for convergence (a.s. or with positive probability) of the response sequence, which is what ‘learning' means.



1984 ◽  
Vol 15 (2) ◽  
pp. 249-262 ◽  
Author(s):  
Wiltrud Mühleis


Stochastics ◽  
2010 ◽  
Vol 82 (5) ◽  
pp. 445-474 ◽  
Author(s):  
Son Luu Nguyen ◽  
G. Yin


1980 ◽  
Vol 12 (04) ◽  
pp. 922-941
Author(s):  
Peter Findeisen

One general and three specialized models of the Bush–Mosteller type are presented to describe the kind of learning experiment where the response of the learner is always reinforced. Inhomogeneity is admitted. The random sequences of response probabilities and of responses associated with the different models are considered. Information about the existence and the distribution of asymptotic response probabilities is provided. The stress is on sufficient and necessary conditions for convergence (a.s. or with positive probability) of the response sequence, which is what ‘learning' means.





2016 ◽  
Author(s):  
Alejandro Francetich ◽  
David M. Kreps


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