We consider the critical branching processes in correlated random environment which is positively associated and study the probability of survival up to the $n$-th generation. Moreover, when the environment is given by fractional Brownian motion, we estimate also the tail of progeny as well as the tail of width.
"Branching processes in correlated random environment." Electron. Commun. Probab. 24 1 - 13, 2019. https://doi.org/10.1214/19-ECP268