Precise large deviations for dependent regularly varying sequences
نویسندگان
چکیده
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 [44] and S.V. Nagaev [45] for iid regularly varying sequences. The proof uses an idea of Jakubowski [28, 29] in the context of central limit theorems with infinite variance stable limits. We illustrate the principle for stochastic volatility models, functions of a Markov chain satisfying a polynomial drift condition and solutions of linear and non-linear stochastic recurrence equations. AMS 2000 subject classifications: Primary 60F10; Secondary 60J05, 60G70
منابع مشابه
A large deviations approach to limit theory for heavy-tailed time series
In this paper we propagate a large deviations approach for proving limit theory for (generally) multivariate time series with heavy tails. We make this notion precise by introducing regularly varying time series. We provide general large deviation results for functionals acting on a sample path and vanishing in some neighborhood of the origin. We study a variety of such functionals, including l...
متن کاملHenrik Hult , Filip Lindskog and Thomas Mikosch : Functional large deviations for multivariate regularly varying random walks
We extend classical results by A.V. Nagaev (1969) on large deviations for sums of iid regularly varying random variables to partial sum processes of iid regularly varying vectors. The results are stated in terms of a heavy-tailed large deviation principle on the space of càdlàg functions. We illustrate how these results can be applied to functionals of the partial sum process, including ruin pr...
متن کاملThe cluster index of regularly varying sequences with applications to limit theory for functions of multivariate Markov chains
We introduce the cluster index of a multivariate regularly varying stationary sequence and characterize the index in terms of the spectral tail process. This index plays a major role in limit theory for partial sums of regularly varying sequences. We illustrate the use of the cluster index by characterizing infinite variance stable limit distributions and precise large deviation results for sum...
متن کاملRare-event Simulation for Multidimensional Regularly Varying Random Walks
We consider the problem of e¢ cient estimation via simulation of rst passage time probabilities for a multidimensional random walk with regularly varying increments. In addition of being a natural generalization of the problem of computing ruin probabilities in insurance in which the focus is a one dimensional random walk this problem captures important features of large deviations for multi...
متن کاملState-dependent Importance Sampling for Regularly Varying Random Walks
Consider a sequence (Xk : k ≥ 0) of regularly varying independent and identically distributed random variables with mean 0 and finite variance. We develop efficient rare-event simulation methodology associated with large deviation probabilities for the random walk (Sn : n ≥ 0). Our techniques are illustrated by examples, including large deviations for the empirical mean and path-dependent event...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2011