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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Official URL: https://doi.org/10.1214/23-EJP907

Анотація

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.

Тип файлу:	Стаття
Ключові слова:	exponential functional of Brownian motion; functional central limit theorem; law of the iterated logarithm; perpetuity
Теми:	За напрямами > Математика та природничі науки
Підрозділи:	Економічний факультет > Кафедра економіко-математичного моделювання та інформаційних технологій
Розмістив/ла:	Anatolii Nikitin
Дата розміщення:	15 Бер 2024 09:35
Остання зміна:	15 Бер 2024 09:35
URI:	https://eprints.oa.edu.ua/id/eprint/9055

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