Asymptotic behavior for iterated functions of random variables (Q1578599)

The authors' main result provides some relaxed conditions under which certain asymptotics, in particular weak laws of large numbers, hold for a hierarchical sequence defined via iterated functions. The construction starts from a strictly stationary and \(m\)-dependent sequence on a closed domain on the real line, and is then iterated under functions satisfying certain subadditive constraints. Under stronger conditions, the authors also obtain a strong law of large numbers. A series of examples, comments and open problems is discussed which are related to hierarchical models in various applications.