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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## Abstract

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 |
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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 |

URI: | https://eprints.oa.edu.ua/id/eprint/9055 |

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