Iteration of IID random maps on $\bold R\sp +$
Krishna Balasundaram Athreya · Lecture notes-monograph series · 2003
Let {X n } be a Markov chain on R + generated by the iteration scheme Xn+i = C n +iX n g(X u ), where {C n ,g n (-)} are i.i.d.such that {C n } are nonnegative r.v. with values in [0, L], L • [0,1] with g n (0) = 1.This paper presents a survey of recent results on the existence of nontrivial stationary measures, Harris irreducibility and uniqueness of stationary measures, convergence and persistence.Four well known special cases i.e. the logistic, Ricker, Hassel and Vellekoop-Hognas models are discussed.