scholarly journals The State Space Isomorphism Theorem for Discrete-Time Infinite-Dimensional Systems

2015 ◽  
Vol 84 (1) ◽  
pp. 105-120
Author(s):  
Amine N. Chakhchoukh ◽  
Mark R. Opmeer
Keyword(s):  
State Space ◽  
Discrete Time ◽  
The State ◽  
Isomorphism Theorem ◽  
Infinite Dimensional ◽  
Infinite Dimensional Systems

Lumpability for non-irreducible finite markov chains

1984 ◽  
Vol 21 (03) ◽  
pp. 567-574 ◽  
Author(s):  
Atef M. Abdel-Moneim ◽  
Frederick W. Leysieffer
Keyword(s):  
Markov Chain ◽  
Markov Chains ◽  
State Space ◽  
Discrete Time ◽  
The State ◽  
Discrete Time Markov Chain ◽  
Finite Markov Chains

Conditions under which a function of a finite, discrete-time Markov chain, X(t), is again Markov are given, when X(t) is not irreducible. These conditions are given in terms of an interrelationship between two partitions of the state space of X(t), the partition induced by the minimal essential classes of X(t) and the partition with respect to which lumping is to be considered.

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