Affine stochastic recursions and stable laws (Q1942082)

The paper deals with affine stochastic recursions \(X_0^x = x\), \(X_{n + 1}^x = {a_{n + 1}}X_n^x + {b_n} = {h_n}(X_n^x)\), where \(X_n^x\) take values in \(d\)-dimensional Euclidean space \(V\), and \({h_n}\) are i.i.d. elements taking values in the group of affine transforms of \(V\). It gives conditions for the sums \(S_n^x = \sum\nolimits_{k = 1}^n {X_k^x} \) to converge in distribution to a stable law.