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2023 Limit theorems for discounted convergent perpetuities II
Alexander Iksanov, Alexander Marynych, Anatolii Nikitin
Author Affiliations +
Electron. J. Probab. 28: 1-22 (2023). DOI: 10.1214/23-EJP907


Let (ξ1,η1), (ξ2,η2), be independent identically distributed R2-valued random vectors. Assuming that ξ1 has zero mean and finite variance and imposing three distinct groups of assumptions on the distribution of η1 we prove three functional limit theorems for the logarithm of convergent discounted perpetuities k0eξ1++ξkakηk+1 as a0+. 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.

Funding Statement

A. Iksanov and A. Marynych were supported by the National Research Foundation of Ukraine (project 2020.02/0014 ‘Asymptotic regimes of perturbed random walks: on the edge of modern and classical probability’).


We thank the anonymous referee for many useful suggestions which greatly improved the presentation of our results.


Download Citation

Alexander Iksanov. Alexander Marynych. Anatolii Nikitin. "Limit theorems for discounted convergent perpetuities II." Electron. J. Probab. 28 1 - 22, 2023.


Received: 2 August 2022; Accepted: 16 January 2023; Published: 2023
First available in Project Euclid: 20 January 2023

MathSciNet: MR4536690
zbMATH: 1508.60040
MathSciNet: MR4529085
Digital Object Identifier: 10.1214/23-EJP907

Primary: 60F15 , 60F17
Secondary: 60G50 , 60G55

Keywords: exponential functional of Brownian motion , functional central limit theorem , Law of the iterated logarithm , perpetuity

Vol.28 • 2023
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