Limit theorems for discounted convergent perpetuities II

Let ( ξ 1 , η 1 ), ( ξ 2 , η 2 ) , . . . be independent identically distributed R 2 -valued random vectors. Assuming that ξ 1 has zero mean and finite variance and imposing three distinct groups of assumptions on the distribution of η 1 we prove three functional limit theorems for the logarithm of convergent discounted perpetuities P k ≥ 0 e ξ 1 + ... + ξ k − ak η k +1 as a → 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.