Precise large deviations for dependent regularly varying sequences.

Thomas Mikosch (1) , Olivier Wintenberger (2)

1 Laboratory of Actuarial Mathematics
2 CEREMADE - CEntre de REcherches en MAthématiques de la DEcision

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.

Mots clés: stationary sequence; large deviation principle; regular variation; Markov processes; stochastic volatility model; GARCH; GARCH.

Domaines: Statistiques [math.ST]; Probabilités [math.PR]; Théorie [stat.TH]

Thomas Mikosch, Olivier Wintenberger. Precise large deviations for dependent regularly varying sequences.. Probability Theory and Related Fields, 2012, 156 (3-4), pp.851-887. ⟨10.1007/s00440-012-0445-0⟩. ⟨hal-00705107⟩