标题： 精确的大偏差：依赖的正则变化序列 显示英文标题

标题： Precise large deviations for dependent regularly varying sequences

摘要： 我们研究了平稳正则变化随机变量序列的一个精确的大偏差原理。 这一原理扩展了A.V. Nagaev（1969）和S.V. Nagaev（1979）的经典结果，适用于独立同分布的正则变化序列。 证明使用了Jakubowski（1993,1997）在无限方差稳定极限中心极限定理中的思想。 我们将这一原理应用于\sv 模型、满足多项式漂移条件的马尔可夫链函数以及线性和非线性随机递归方程的解。 显示英文摘要

摘要： We study a precise large deviation principle for a stationary regularly varying sequence of random variables. This principle extends the classical results of A.V. Nagaev (1969) and S.V. Nagaev (1979) for iid regularly varying sequences. The proof uses an idea of Jakubowski (1993,1997) in the context of centra limit theorems with infinite variance stable limits. We illustrate the principle for \sv\ models, functions of a Markov chain satisfying a polynomial drift condition and solutions of linear and non-linear stochastic recurrence equations.