Tag Archives: law of large numbers

Law of large numbers for dependent but uncorrelated random variables

Posted on February 5, 2014 by Vaughn Climenhaga

One of the fundamental results in probability theory is the strong law of large numbers, which was discussed in an earlier post under the guise of the Birkhoff ergodic theorem. Suppose we have a sequence of random variables which take … Continue reading →

Posted in statistical laws, theorems | Tagged | 4 Comments

Laws of large numbers and Birkhoff’s ergodic theorem

Posted on March 9, 2013 by Vaughn Climenhaga

In preparation for the next post on the central limit theorem, it’s worth recalling the fundamental results on convergence of the average of a sequence of random variables: the law of large numbers (both weak and strong), and its strengthening … Continue reading →

Posted in ergodic theory, statistical laws, theorems | Tagged | 7 Comments