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Precise large deviations for dependent regularly varying sequences

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
Publication identifier
http://dx.doi.org/10.1007/s00440-012-0445-0
Metadata
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Author(s)
Wintenberger, Olivier
Mikosch, Thomas
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

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