具有无限记忆的弱相依链
Weakly dependent chains with infinite memory
摘要：
证明了方程$ X_t=F(X_{t-1},X_{t-2},X_{t-3},...;ξ_t)$的弱相依严格平稳解的存在性，称之为{具有无限记忆的\em链}.这里，{ \em新息} $ξ_t$构成独立且同分布的随机变量序列。函数$F$在某些巴拿赫空间中取值，并满足Lipschitz型条件。我们还研究了存在的时刻和衰减率的函数$F$的Lipschitz系数之间的相互作用。利用弱相依性质，我们得到了强大数定律、中心极限定理和强不变原理。
英文摘要：
We prove the existence of a weakly dependent strictly stationary solution of the equation $ X_t=F(X_{t-1},X_{t-2},X_{t-3},...;ξ_t)$ called {\em chain with infinite memory}. Here the {\em innovations} $ξ_t$ constitute an independent and identically distributed sequence of random variables. The function $F$ takes values in some Banach space and satisfies a Lipschitz-type condition. We also study the interplay between the existence of moments and the rate of decay of the Lipschitz coefficients of the function $F$. With the help of the weak dependence properties, we derive Strong Laws of Large Number, a Central Limit Theorem and a Strong Invariance Principle.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
