Limit theorems for random walks with dynamical random transitions

Abstract

Let θ be an ergodic and conservative non-singular transformation of (Ω, Σ,m) (thedynamic environment), let μ w be a random probability on a locally compact second countable groupG, and define $$v_{_w }^{(n)} = \mu _{\theta ^n } - 1_w *\mu _{\theta ^n } - 2_w *...*\mu _{\theta w} *\mu _w $$