论文标题
符号随机差方程的渐近渐进式变化
Slowly varying asymptotics for signed stochastic difference equations
论文作者
论文摘要
对于随机差方程，$ d_n = a_nd_ {n-1}+b_n $在我们研究尾巴分布渐近造成$ d_n $的情况下稳定下来，假设$ \ log的分布（1+| a_1 | a_1 |+|+| b_1 |）$是重量的，这就是其所有积极的付出量的iNSents Inments Insents Insents Insents Insente insents insents insents insents insents insents insents Insentent。本文的目的是三倍。首先，我们不仅确定了固定尾巴分布的渐近行为，而且还确定$ d_n $的渐近行为。其次，当$ a $同时获得正值和负值时，我们在一般环境中解决了问题。第三，我们摆脱了辅助条件，例如以前在文献中使用的较高时刻的有限性。
For a stochastic difference equation $D_n=A_nD_{n-1}+B_n$ which stabilises upon time we study tail distribution asymptotics of $D_n$ under the assumption that the distribution of $\log(1+|A_1|+|B_1|)$ is heavy-tailed, that is, all its positive exponential moments are infinite. The aim of the present paper is three-fold. Firstly, we identify the asymptotic behaviour not only of the stationary tail distribution but also of $D_n$. Secondly, we solve the problem in the general setting when $A$ takes both positive and negative values. Thirdly, we get rid of auxiliary conditions like finiteness of higher moments used in the literature before.
