Limit theorems for discounted convergent perpetuities II

Let (ξ1,η1), (ξ2,η2),… be independent identically distributed R2-valued random vectors. Assuming that ξ1 has zero mean and finite variance imposing three distinct groups of assumptions on the distribution η1 we prove functional limit theorems for logarithm convergent discounted perpetuities ∑k≥0eξ1+…+ξk−akη k+1 as a→0+. Also, a law iterated which corresponds to one aforementioned theorems. The present paper continues line research initiated in Iksanov, Nikitin Samoillenko (2022), focused different type perpetuities.