A ``multiplicative coboundary'' theorem for some sequences of random matrices
\textit{K. Schmidt} [``Cocycles of ergodic transformation groups'' (1977; Zbl 0421.28017)] proved the following result: Suppose the sequence \((X(k),\;k\) an integer) is a strictly stationary sequence of real random variables such that the family of distributions of the partial sums \((X(1)+\dots +X(n),\;n=1,2,3,\dots)\) is tight; then there exists a Borel function \(f\) on the infinite product (of copies of \(R\)) such that if \(Y(k)=f(X(k),X(k+1),\dots)\), then for every integer \(k\), one has almost surely \(X(k)=Y(k)-Y(k+1)\). A strictly stationary sequence \((X(k))\) is called a ``coboundary'' if it has the representation just mentioned. The author proves an analog of Schmidt's result for some sequences of random matrices, with partial sums replaced by matrix products.
scientific article; zbMATH DE number 934233
scientific article