论文标题
限制定理的折扣收敛永久性ii
Limit theorems for discounted convergent perpetuities II
论文作者
论文摘要
令$（ξ_1，η_1）$，$（ξ_2，η_2），\ ldots $是独立分布的$ \ mathbb {r}^2 $ - 价值的随机向量。假设$ξ_1$具有零均值和有限差异，并且对$η_1$的分布施加了三个不同的假设，那么我们证明了三个功能限制定理的三个功能限制定理，用于收敛性打折的永久性$ \ sum_ \ sum_ {k \ geq 0} e^{k \ geq 0} $ a \至0+$。另外，我们证明了迭代对数的定律，该定律与上述功能极限定理之一相对应。本文继续在伊克萨诺夫（Iksanov），尼基丁（Nikitin）和萨莫林科（Samoillenko）（2022）的论文中发起的一系列研究，该研究的重点是限制定理，以不同类型的收敛性折扣永久性。
Let $(ξ_1, η_1)$, $(ξ_2, η_2),\ldots$ be independent identically distributed $\mathbb{R}^2$-valued random vectors. Assuming that $ξ_1$ has zero mean and finite variance and imposing three distinct groups of assumptions on the distribution of $η_1$ we prove three functional limit theorems for the logarithm of convergent discounted perpetuities $\sum_{k\geq 0}e^{ξ_1+\ldots+ξ_k-ak}η_{k+1}$ as $a\to 0+$. 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.
