Precise large deviations for dependent regularly varying sequences

• 成果类型: Article
• 署名作者: Mikosch, Thomas; Wintenberger, Olivier
• 署名单位: University of Copenhagen; Universite PSL; Universite Paris-Dauphine
• 刊物名称: PROBABILITY THEORY AND RELATED FIELDS
• ISSN/ISSBN: 0178-8051
• DOI: 10.1007/s00440-012-0445-0
• 发表日期: 2013
• 页码: 851-887
• 关键词: minimal conditions; random-variables; LIMIT-THEOREMS; CONVERGENCE; recurrence; EQUATIONS; ruin; sums

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 Nagaev (Theory Probab Appl 14:51-64, 193-208, 1969) and Nagaev (Ann Probab 7:745-789, 1979) for iid regularly varying sequences. The proof uses an idea of Jakubowski (Stoch Proc Appl 44:291-327, 1993; 68:1-20, 1997) in the context of central limit theorems with infinite variance stable limits. We illustrate the principle for stochastic volatility models, real valued functions of a Markov chain satisfying a polynomial drift condition and solutions of linear and non-linear stochastic recurrence equations.