scholarly journals Ergodic decomposition

2020 ◽  
Author(s):  
Sakshi Jain ◽  
Shah Faisal
Keyword(s):  
Ergodic Decomposition

scholarly journals Ergodic decomposition of group actions on rooted trees

2016 ◽  
Vol 292 (1) ◽  
pp. 94-111 ◽  
Author(s):  
Rostislav Grigorchuk ◽  
Dmytro Savchuk
Keyword(s):  
Group Actions ◽  
Rooted Trees ◽  
Ergodic Decomposition

Ergodic decomposition of probability laws

1981 ◽  
Vol 56 (3) ◽  
pp. 399-414 ◽  
Author(s):  
Johannes Kerstan ◽  
Anton Wakolbinger
Keyword(s):  
Ergodic Decomposition

scholarly journals On the ergodic decomposition for a cocycle

2009 ◽  
Vol 117 (1) ◽  
pp. 121-156 ◽  
Author(s):  
Jean-Pierre Conze ◽  
Albert Raugi
Keyword(s):  
Ergodic Decomposition

scholarly journals Process Dimension of Classical and Non-Commutative Processes

2012 ◽  
Vol 19 (01) ◽  
pp. 1250007
Author(s):  
Wolfgang Löhr ◽  
Arleta Szkoła ◽  
Nihat Ay
Keyword(s):  
Stochastic Process ◽  
Ergodic Decomposition ◽  
Statistical Complexity ◽  
Lower Semi ◽  
Decomposition Formula ◽  
Close Relationship ◽  
Natural Characteristic ◽  
Causal States ◽  
Definition Of ◽  
Process Dimension

We treat observable operator models (OOM) and their non-commutative generalisation, which we call NC-OOMs. A natural characteristic of a stochastic process in the context of classical OOM theory is the process dimension. We investigate its properties within the more general formulation, which allows one to consider process dimension as a measure of complexity of non-commutative processes: We prove lower semi-continuity, and derive an ergodic decomposition formula. Further, we obtain results on the close relationship between the canonical OOM and the concept of causal states which underlies the definition of statistical complexity. In particular, the topological statistical complexity, i.e. the logarithm of the number of causal states, turns out to be an upper bound to the logarithm of process dimension.

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