Strong solutions of Tsirel'son's equation in discrete time taking values in compact spaces with semigroup action (Q1950709)

Let \(\Sigma\) be a compact topological semigroup acting on some compact space \(S\). For a given sequence \((N_k)_{k\in-\mathbb N}\) of independent \(\Sigma\)-valued variables, the authors study whether the stochastic recurrence equation \(X_k=N_kX_{k-1}\) for \(k\in-\mathbb N\) admits a solution. It turns out that a solution exists if \(\lim_{l\to-\infty} N_k\dotsm N_{l+1}\) exists almost surely for all \(k\in-\mathbb N\).