Precise large deviations for dependent regularly varying sequences

Wintenberger, Olivier; Mikosch, Thomas

Wintenberger, Olivier; Mikosch, Thomas (2013), Precise large deviations for dependent regularly varying sequences, Probability Theory and Related Fields, 156, 3-4, p. 851-887. http://dx.doi.org/10.1007/s00440-012-0445-0

Type

Article accepté pour publication ou publié

External document link

http://hal.archives-ouvertes.fr/hal-00705107

Date

2013

Journal name

Probability Theory and Related Fields

Volume

156

Number

3-4

Publisher

Springer

Pages

851-887

Abstract (EN)

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.

Subjects / Keywords

GARCH; stochastic volatility model; Markov processes; regular variation; large deviation principle; stationary sequence