Elementary fixed points of the BRW smoothing transforms with infinite number of summands

Aleksander M. Iksanov

The branching random walk (BRW) smoothing transform $T$ is defined as $T:\text{distr}(U_1)\mapsto \text{distr}({\sum }_{i=1}^L{X}_i{U}_i)$, where given realizations $\{X_{i}\}_{i…