¡div class=”moz-text-flowed” style=”font-family: -moz-fixed”¿

For real numbers C, T 1 , T 2 , ... we find all solutions µ to the stochastic fixed point equation W j≥1 T j W j + C, where W, W 1 , W 2 , ... are independent real-valued random variables with distribution µ and means equality in distribution. All solutions are infinitely divisible. The set of solutions depends on the closed multiplicative subgroup of R * = R\{0} generated by the T j. If this group is continuous, i.e. R * itself or the positive halfline R > , then all nontrivial fixed points are stable laws. In the remaining (discrete) cases further periodic solutions arise. A key observation is that the Lévy measure of any fixed point is harmonic with respect to Λ = j≥1 δ T j , i.e. Γ = Γ ⋆ Λ, where ⋆ means multiplicative convolution. This will enable us to apply the powerful Choquet-Deny theorem.