SELF-NORMALIZED WEAK LIMIT THEOREMS FOR A ø-MIXING SEQUENCE
نویسندگان
چکیده
منابع مشابه
Self-normalized Weak Limit Theorems for a Φ-mixing Sequence
Let {Xj , j ≥ 1} be a strictly stationary φ-mixing sequence of non-degenerate random variables with EX1 = 0. In this paper, we establish a self-normalized weak invariance principle and a central limit theorem for the sequence {Xj} under the condition that L(x) := EX2 1 I{|X1| ≤ x} is a slowly varying function at ∞, without any higher moment conditions.
متن کاملSelf-normalized limit theorems: A survey
Let X1,X2, . . . , be independent random variables with EXi = 0 and write Sn = ∑ n i=1 Xi and V 2 n = ∑ n i=1 X i . This paper provides an overview of current developments on the functional central limit theorems (invariance principles), absolute and relative errors in the central limit theorems, moderate and large deviation theorems and saddle-point approximations for the self-normalized sum S...
متن کاملLimit Theorems for Self-Similar Tilings
We study deviation of ergodic averages for dynamical systems given by self-similar tilings on the plane and in higher dimensions. The main object of our paper is a special family of finitely-additive measures for our systems. An asymptotic formula is given for ergodic integrals in terms of these finitely-additive measures, and, as a corollary, limit theorems are obtained for dynamical systems g...
متن کاملA Limit Theorem for the Moment of Self-Normalized Sums
Qing-pei Zang Department of Mathematics, Huaiyin Teachers College, Huaian 223300, China Correspondence should be addressed to Qing-pei Zang, [email protected] Received 25 December 2008; Revised 30 March 2009; Accepted 18 June 2009 Recommended by Jewgeni Dshalalow Let {X,Xn;n ≥ 1} be a sequence of independent and identically distributed i.i.d. random variables and X is in the domain of attra...
متن کاملStrong limit theorems for partial sums of a random sequence
Let {ξj ; j ≥ 1} be a centered strictly stationary random sequence defined by S0 = 0, Sn = ∑n j=1 ξj and σ(n) = √ ES2 n, where σ(t), t > 0, is a nondecreasing continuous regularly varying function. Suppose that there exists n0 ≥ 1 such that, for any n ≥ n0 and 0 ≤ ε < 1, there exist positive constants c1 and c2 such that c1 e−(1+ε)x 2/2 ≤ P { |Sn| σ(n) ≥ x } ≤ c2 e −(1−ε)x2/2, x ≥ 1. Under some...
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: Bulletin of the Korean Mathematical Society
سال: 2010
ISSN: 1015-8634
DOI: 10.4134/bkms.2010.47.6.1139