Construction of a Model of Gaussian Stationary Random Process in Some Orlicz Spaces with Given Accuracy and Reliability

2017 ◽  
Author(s):  
Yu.V. Kozachenko ◽  
A.M. Tegza
Keyword(s):  
Random Process ◽  
Orlicz Spaces ◽  
Stationary Random Process

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.

A test for a stationary random process

1977 ◽  
Vol 60 (4) ◽  
pp. 281-282 ◽  
Author(s):  
P. Kittel
Keyword(s):  
Random Process ◽  
Stationary Random Process
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