Stable fluctuations of iterated perturbed random walks in intermediate generations of a general branching process tree

Alexander Iksanov, Alexander Marynych, Bohdan Rashytov

Consider a general branching process, a.k.a. Crump-Mode-Jagers process, generated by a perturbed random walk ${\eta }_1$, ${\xi }_1+{\eta }_2$, ${\xi }_1+{\xi }_2+{\eta }_3,\dots$. Here, $({\xi }_1,{\eta }_1)$, $(ξ_2, η_2),…