Relative entropy densities and a class of limit theorems of the sequence of m-valued random variables (Q923481)

Let \(\{X_ n\), \(n\geq 1\}\) be a sequence of random variables taking values in \(S=\{1,2,...,m\}\) with the joint distribution \(P(X_ 1=x_ 1,...,X_ n=x_ n)=p(x_ 1,...,x_ n)>0.\) Let \(\phi_ n=n^{-1}\log p(X_ 1,...,X_ n)\) be the relative entropy density of \(\{X_ k\), \(1\leq k\leq n\}\). The relation between the relative entropy and a class of limit theorems is studied.