Stochastic Recursive Sequences

Abstract

The chapter begins with introducing the concept of stochastic random sequences in Sect. 17.1. The idea of renovating events together with the key results on ergodicity of stochastic random sequences and the boundedness thereof is presented in Sect. 17.2, whereas the Loynes ergodic theorem for the case of monotone functions specifying the recursion is proved in Sect. 17.3. Section 17.4 establishes ergodicity conditions for contracting in mean Lipschitz transformations.