A REPRESENTATION OF MARTINGALE DIFFERENCES AND ORTHONORMAL SYSTEMS OF UNCONDITIONAL CONVERGENCE ALMOST EVERYWHERE

2000 ◽  
Vol 26 (1) ◽  
pp. 311
Author(s):  
Krantsberg
Keyword(s):  
Unconditional Convergence ◽  
Martingale Differences ◽  
Convergence Almost Everywhere ◽  
Almost Everywhere

scholarly journals Strong Law of Large Numbers of the Offspring Empirical Measure for Markov Chains Indexed by Homogeneous Tree

2012 ◽  
Vol 2012 ◽  
pp. 1-9
Author(s):  
Huilin Huang
Keyword(s):  
Markov Chains ◽  
Law Of Large Numbers ◽  
Empirical Measure ◽  
Homogeneous Tree ◽  
Almost Everywhere Convergence ◽  
Strong Law ◽  
Convergence Almost Everywhere ◽  
Almost Everywhere ◽  
Large Numbers

We study the limit law of the offspring empirical measure and for Markov chains indexed by homogeneous tree with almost everywhere convergence. Then we prove a Shannon-McMillan theorem with the convergence almost everywhere.

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