Limit theorems for discounted convergent perpetuities II

Let (& xi;1, & eta;1), (& xi;2, & eta;2), ... be independent identically distributed R2-valued random vec-tors. Assuming that & xi;1 has zero mean and finite variance and imposing three distinct groups of assumptions on the distribution of & eta;1 we prove three functional limit theo-rems for the logarithm of convergent discounted perpetuities Ek & GE;0 e & xi;1+...+& xi;k-ak & eta;k+1 as a & RARR; 0+. Also, we prove a law of the iterated logarithm which corresponds to one of the aforementioned functional limit theorems. The present paper continues a line of research initiated in the paper Iksanov, Nikitin and Samoillenko (2022), which focused on limit theorems for a different type of convergent discounted perpetuities.