Precise asymptotics in the law of logarithm under dependence assumptions
نویسندگان
چکیده
Keywords: Law of the logarithm Mixing sequences Precise asymptotics Strong approximation Stationary a b s t r a c t In a recent paper by Spătaru [Precise asymptotics for a series of T. a precise asymptotics in the law of the logarithm for sequence of i.i.d. random variables has been established. In this paper we show that there is an analogous result for strictly stationary ϕ-mixing sequence. To prove this result, we have to use a different method. One of our main tools is the Gaussian approximation technique.
منابع مشابه
Precise Asymptotics for the Moment Convergence of Moving-average Process under Dependence
Let {εi : −∞ < i < ∞} be a strictly stationary sequence of linearly positive quadrant dependent random variables and P∞ i=−∞ |ai| < ∞. In this paper, we prove the precise asymptotics in the law of iterated logarithm for the moment convergence of moving-average process of the form Xk = P∞ i=−∞ ai+kεi, k ≥ 1.
متن کاملA Supplement to Precise Asymptotics in the Law of the Iterated Logarithm for Self-normalized Sums
Let X, X1, X2, . . . be i.i.d. random variables with zero means, variance one, and set Sn = ∑n i=1 Xi, n ≥ 1. Gut and Spǎtaru [3] established the precise asymptotics in the law of the iterated logarithm and Li, Nguyen and Rosalsky [7] generalized their result under minimal conditions. If P(|Sn| ≥ ε √ 2n log log n) is replaced by E{|Sn|/√n− ε √ 2 log log n}+ in their results, the new one is call...
متن کاملPrecise asymptotics in laws of the iterated logarithm for Wiener local time
In this paper, we study the asymptotic properties of the upper and lower tail probabilities of the maximum local time L∗(t) of Wiener process (Brownian motion), and obtain some precise asymptotics in the law of the iterated logarithm and the Chungs-type laws of the iterated logarithm for the supremum of Wiener local time L(x; t); x∈R; t ∈R+. c © 2003 Elsevier B.V. All rights reserved. MSC: 60F1...
متن کاملPrecise Asymptotics in the Law of the Iterated Logarithm under Dependence
Let {X n ; n ≥ 1} be a strictly stationary negatively associated sequence which satisfies EX 1 = 0, V ar(X 1) < ∞. Set S n = n k=1 X k , n ≥ 1, σ 2 = EX 2 1 + 2 ∞ k=2 EX 1 X k. In this paper, we prove that, for b > −1, lim ε0 ε 2(b+1) ∞ n=1 (log log n) b n log n P{|S n | ≥ εσ n log log n} = 2 b+1 (b + 1) √ π Γ(b + 3 2) holds if EX 2 1 (1 + log log |X 1 |) b−1 < ∞. The result of Gut and Spˇataru...
متن کاملAsymptotic Behaviors of the Lorenz Curve for Left Truncated and Dependent Data
The purpose of this paper is to provide some asymptotic results for nonparametric estimator of the Lorenz curve and Lorenz process for the case in which data are assumed to be strong mixing subject to random left truncation. First, we show that nonparametric estimator of the Lorenz curve is uniformly strongly consistent for the associated Lorenz curve. Also, a strong Gaussian approximation for ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید
ثبت ناماگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید
ورودعنوان ژورنال:
- Computers & Mathematics with Applications
دوره 56 شماره
صفحات -
تاریخ انتشار 2008