On Hankel-Norm Approximation of Large-Scale Markov Chains

1991 ◽  
Author(s):  
Guanrong Chen ◽  
Charles K. Chui ◽  
Yaoqi Yu
Keyword(s):  
Markov Chains ◽  
Large Scale ◽  
Hankel Norm ◽  
Norm Approximation

ERROR BOUNDS FOR OCCUPATION MEASURE OF SINGULARLY PERTURBED MARKOV CHAINS INCLUDING TRANSIENT STATES

2000 ◽  
Vol 14 (4) ◽  
pp. 511-531 ◽  
Author(s):  
G. Yin ◽  
Q. Zhang ◽  
Q. G. Liu
Keyword(s):  
Markov Chains ◽  
Error Bounds ◽  
Queueing Networks ◽  
Large Scale ◽  
Singularly Perturbed ◽  
Planning System ◽  
Nonstationary Processes ◽  
Transient States ◽  
Asymptotic Error ◽  
Occupation Measures

Motivated by many applications in production planning, system reliability, queueing networks, and wireless communication, this work is devoted to singularly perturbed Markov chains with finite states. Focusing on nonstationary processes with the inclusion of transient states, asymptotic error bounds of a sequence of suitably scaled occupation measures are derived. The main tools used include martingales and differential equations. The results are useful for analyzing structural properties of the underlying Markov chains and for designing nearly optimal and hierarchical controls of large-scale and complex systems.

On the transformation formulas of the Hankel-norm approximation

PAMM ◽  
2017 ◽  
Vol 17 (1) ◽  
pp. 823-824
Author(s):  
Peter Benner ◽  
Steffen W. R. Werner
Keyword(s):  
Hankel Norm ◽  
Transformation Formulas ◽  
Norm Approximation
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