Comment on “a non-stationary random process model for earthquake accelerograms,” by R. N. Iyengar and K. T. S. R. Iyengar

1983 ◽  
Vol 73 (3) ◽  
pp. 887-887
Author(s):  
G. R. Dargahi-Noubary
Keyword(s):  
Random Process ◽  
Process Model ◽  
Stationary Random Process ◽  
Earthquake Accelerograms

Induced transformations of recurrent a.m.s. dynamical systems

2015 ◽  
Vol 15 (02) ◽  
pp. 1550010
Author(s):  
Sheng Huang ◽  
Mikael Skoglund
Keyword(s):  
Dynamical System ◽  
Dynamical Systems ◽  
Random Process ◽  
Ergodic Theorem ◽  
Finite Measure ◽  
Stationary Random Process ◽  
Finite State ◽  
Ratio Ergodic Theorem

This note proves that an induced transformation with respect to a finite measure set of a recurrent asymptotically mean stationary dynamical system with a sigma-finite measure is asymptotically mean stationary. Consequently, the Shannon–McMillan–Breiman theorem, as well as the Shannon–McMillan theorem, holds for all reduced processes of any finite-state recurrent asymptotically mean stationary random process. As a by-product, a ratio ergodic theorem for asymptotically mean stationary dynamical systems is presented.

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