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- W4289785100 abstract "Let $(xi_1, eta_1)$, $(xi_2, eta_2),ldots$ be independent identically distributed $mathbb{R}^2$-valued random vectors. 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 theorems for the logarithm of convergent discounted perpetuities $sum_{kgeq 0}e^{xi_1+ldots+xi_k-ak}eta_{k+1}$ as $ato 0+$. 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." @default.
- W4289785100 created "2022-08-04" @default.
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- W4289785100 date "2022-08-02" @default.
- W4289785100 modified "2023-09-24" @default.
- W4289785100 title "Limit theorems for discounted convergent perpetuities II" @default.
- W4289785100 doi "https://doi.org/10.48550/arxiv.2208.01609" @default.
- W4289785100 hasPublicationYear "2022" @default.
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