Limit theorems for discounted convergent perpetuities II

Iksanov, Alexander and Marynych, Alexander and Nikitin, Anatolii (2023) Limit theorems for discounted convergent perpetuities II. Electronic Journal of Probability, 28. pp. 1-22. ISSN 1083-6489

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

Item Type: Article
Uncontrolled Keywords: exponential functional of Brownian motion; functional central limit theorem; law of the iterated logarithm; perpetuity
Subjects: by fields of science > Mathematics
Divisions: The College of Economics Management > Department of Economic-Mathematical Modeling and Information Technologies
Depositing User: Anatolii Nikitin
Date Deposited: 15 Mar 2024 09:35
Last Modified: 15 Mar 2024 09:35

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