Precise large deviations for dependent regularly varying sequences

2012/06/07 by Thomas Mikosch, Olivier Wintenberger, Mikosch, Thomas +1 · 1 citation
Decision Sciences · Economics, Econometrics and Finance · Mathematics · #FOS: Mathematics #Financial Risk and Volatility Modeling #Probability (math.PR) #Probability and Risk Models #Statistics Theory (math.ST) #Stochastic processes and statistical mechanics

paper · doi:10.48550/arxiv.1206.1395

openalex publication_date 2012/06/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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.

Citations

• Regular variation of GARCH processes

Cited by

• Clustering of large deviations in heavy-tailed moving averages: the catastrophe principle in the long-memory case

Related

• Precise large deviations for dependent subexponential variables
• The central limit theorem for m-dependent variables
• A conditional strong large deviation result and a functional central limit theorem for the rate function
• Precise local large deviations for random sums with applications
• Precise large deviations through a uniform Tauberian theorem