Precise large deviations for dependent subexponential variables
نویسندگان
چکیده
In this paper, we study precise large deviations for the partial sums of a stationary sequence with subexponential marginal distribution. Our main focus is on distributions which either have regularly varying or lognormal-type tail. We apply results to prove limit theory maxima entries sample covariance matrices.
منابع مشابه
Precise large deviations for widely orthant dependent random variables with different distributions
Let [Formula: see text] be a sequence of random variables with different distributions [Formula: see text]. The partial sums are denoted by [Formula: see text], [Formula: see text]. This paper mainly investigates the precise large deviations of [Formula: see text], for the widely orthant dependent random variables [Formula: see text]. Under some mild conditions, the lower and upper bounds of th...
متن کاملPrecise large deviations for dependent regularly varying sequences
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 stochas...
متن کاملLarge deviations for sums of partly dependent random variables
We use and extend a method by Hoeffding to obtain strong large deviation bounds for sums of dependent random variables with suitable dependency structure. The method is based on breaking up the sum into sums of independent variables. Applications are given to U -statistics, random strings and random graphs.
متن کاملON THE LAWS OF LARGE NUMBERS FOR DEPENDENT RANDOM VARIABLES
In this paper, we extend and generalize some recent results on the strong laws of large numbers (SLLN) for pairwise independent random variables [3]. No assumption is made concerning the existence of independence among the random variables (henceforth r.v.’s). Also Chandra’s result on Cesàro uniformly integrable r.v.’s is extended.
متن کاملPrecise Large Deviations for Sums of Random Variables with Consistently Varying Tails in Multi-risk Models
Assume that there are k types of insurance contracts in an insurance company. The ith related claims are denoted by {Xij , j ≥ 1}, i = 1, . . . , k. In this paper we investigate large deviations for both partial sums S(k; n1, . . . , nk) = ∑ki=1 ∑ni j=1 Xij and random sums S(k; t) = ∑ki=1 ∑Ni(t) j=1 Xij , whereNi(t), i = 1, . . . , k, are counting processes for the claim number. The obtained re...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Bernoulli
سال: 2021
ISSN: ['1573-9759', '1350-7265']
DOI: https://doi.org/10.3150/20-bej1276