Precise large deviations for dependent regularly varying sequences.

TY - JOUR

T1 - Precise large deviations for dependent regularly varying sequences.

AU - Mikosch, Thomas Valentin

AU - Wintenberger, Olivier

PY - 2013/8

Y1 - 2013/8

N2 - We study a precise large deviation principle for a stationary regularly varying sequence of random variables. This principle extends the classical results of Nagaev (Theory Probab Appl 14:51-64, 193-208, 1969) and Nagaev (Ann Probab 7:745-789, 1979) for iid regularly varying sequences. The proof uses an idea of Jakubowski (Stoch Proc Appl 44:291-327, 1993; 68:1-20, 1997) in the context of central limit theorems with infinite variance stable limits. We illustrate the principle for stochastic volatility models, real valued functions of a Markov chain satisfying a polynomial drift condition and solutions of linear and non-linear stochastic recurrence equations.

AB - We study a precise large deviation principle for a stationary regularly varying sequence of random variables. This principle extends the classical results of Nagaev (Theory Probab Appl 14:51-64, 193-208, 1969) and Nagaev (Ann Probab 7:745-789, 1979) for iid regularly varying sequences. The proof uses an idea of Jakubowski (Stoch Proc Appl 44:291-327, 1993; 68:1-20, 1997) in the context of central limit theorems with infinite variance stable limits. We illustrate the principle for stochastic volatility models, real valued functions of a Markov chain satisfying a polynomial drift condition and solutions of linear and non-linear stochastic recurrence equations.

M3 - Journal article

SN - 0178-8051

VL - 156

SP - 851

EP - 887

JO - Probability Theory and Related Fields

JF - Probability Theory and Related Fields

ER -