scholarly journals Accumulated damage evaluation for a piping system by the response factor on non-stationary random process (2nd report, A two-degree-offreedom system).

1988 ◽  
Vol 54 (498) ◽  
pp. 376-384 ◽  
Author(s):  
Masanori SHlNTANI
Keyword(s):  
Random Process ◽  
Stationary Random Process ◽  
Piping System ◽  
Response Factor ◽  
Damage Evaluation ◽  
Accumulated Damage

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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