Precise large deviations for dependent regularly varying sequences

TL;DR

This paper establishes a precise large deviation principle for dependent regularly varying sequences, extending classical iid results to dependent cases with applications to various stochastic models.

Contribution

It extends large deviation principles to dependent regularly varying sequences, incorporating dependence structures and providing applications to Markov chains and stochastic recurrence equations.

Findings

Large deviation principle established for dependent sequences.

Extension of classical iid large deviation results.

Applications demonstrated for Markov models and stochastic recurrences.

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.