符号随机差分方程的慢变渐近性
Slowly varying asymptotics for signed stochastic difference equations
摘要：
对于随时间稳定的随机差分方程$D_n=A_nD_{n-1}+B_n$，在假设$\log(1+|A_1|+|B_1|)$的分布是重尾的，即它的所有正指数矩都是无穷大的条件下，研究了$D_n=A_nD_{n-1}+B_n$的尾分布渐近性.本文件有三个目的。首先，我们不仅确定了平稳尾分布的渐近行为，而且还$D_n$。其次，我们解决了一般情况下，当$A$采取积极和消极的价值观的问题。第三，去掉了以往文献中所使用的高阶矩有限性等辅助条件。
英文摘要：
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.
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