Almost sure convergence of products of $2\times2$ nonnegative matrices

An abstract version of our ASCLT is stated and proven in Section 3, as well as an application to partial sums of non-linear functions of a strongly dependent Gaussian sequence..

As an interesting corollary, we show that, for sequences of random variables lying in a fixed finite sum of Gaussian Wiener chaoses, the almost sure convergence is robust to

The second item of theorem 1.1 is a consequence of inequalities (23) and of the following proposition... This concludes

Recall first that the absolutely continuous invariant measures can be obtained as fixed points for the Perron-Frobenius linear operator L in the space of the densities that have

On the Almost Sure Central Limit Theorem for Vector Martingales: Convergence of Moments and Statistical Applications... Centre de recherche INRIA Paris

Thomas, Asymptotic properties of the columns in the products of nonnegative matrices (2009), download.

Remark 4: In this section, the analysis results in Theorem 3.2 and Corollary 1 offer sufficient conditions under which the augmented system (2.5) with v(t) ≡ 0 is almost

We prove an extension of a result by Peres and Solomyak on almost sure absolute continuity in a class of symmetric Bernoulli