On Inhomogeneous Bernoulli Convolutions and Random Power Series

Abstract

We extend the results of Peres and Solomyak on absolute continuity and singularity of homogeneous Bernoulli convolutions to inhomogeneous ones and generalize the result to random power series given by inhomogeneous Markov chains. In addition we prove an Erd\"{o}s-Salem type theorem for inhomogeneous Bernoulli convolutions.