Renorming divergent perpetuities

Paweł Hitczenko, Jacek Wesołowski

We consider a sequence of random variables $(R_n)$ defined by the recurrence $R_n=Q_n+M_n{R}_{n-1}$, $n\ge 1$, where $R_0$ is arbitrary and $(Q_n,M_n)$, $n\ge 1$, are i.i.d. copies of…