AbstractLet X1,X2,… be a strictly stationary sequence of ρ-mixing random variables with mean zeros and positive, finite variances, set Sn=X1+⋯+Xn. Suppose that limn→∞ESn2/n=σ2>0, ∑n=1∞ρ2/q(2n)<∞, where q>2δ+2. We prove that, if EX12(log+|X1|)δ<∞ for any 0<δ⩽1, thenlimϵ↓0ϵ2δ∑n=2∞(logn)δ−1n2ESn2I(|Sn|⩾ϵσnlogn)=E|N|2δ+2δ, where N is the standard normal random variable
AbstractLet (Xn)n⩾1 be a sequence of real random variables. The local score is Hn=max1⩽i<j⩽n(Xi+⋯+Xj...
AbstractLet γ=0.577215664… denote the Euler–Mascheroni constant, and let the sequence wn(a,b,c,d)=∑k...
Let d μ be a probability measure on the unit circle and d ν be the measure formed by adding a pure...
AbstractLet {X,Xn;n⩾1} be a sequence of i.i.d. random variables with EX=0 and EX2=σ2<∞. Set Sn=∑k=1n...
AbstractLet {X,Xn;n⩾1} be a sequence of i.i.d. random variables taking values in a real separable Hi...
AbstractLet X1,X2,… be i.i.d. random variables with partial sums Sn, n⩾1. The now classical Baum–Kat...
AbstractLet {μ(n),n⩾1} be the associated counting process. In this paper, we prove the precise asymp...
AbstractLet X,X1,X2,… be a sequence of nondegenerate i.i.d. random variables with zero means, set Sn...
Given a real number \u3c4, we study the approximation of \u3c4 by signed harmonic sums \u3c3N(\u3c4)...
AbstractLet {Xn,n≥1} be a strictly stationary sequence of random variables and Mn=max{X1,X2,…,Xn}. A...
AbstractThe goal of this paper is to prove the following asymptotic formula Γ(x)≈2πe−b(x+b)xexp(−x−1...
AbstractLet (xjk:j,k=0,1,2,…) be a double sequence of real or complex numbers, and set σmn:=(m+1)−1(...
Given a probability measure μ supported on some compact set K ⊆ C and with orthonormal polynomials {...
AbstractFirst, a maximal inequality for ψ-mixing sequences is given. By using the maximal inequality...
AbstractLet {X,Xn;n⩾1} be a sequence of real-valued i.i.d. random variables with E(X)=0 and E(X2)=1,...
AbstractLet (Xn)n⩾1 be a sequence of real random variables. The local score is Hn=max1⩽i<j⩽n(Xi+⋯+Xj...
AbstractLet γ=0.577215664… denote the Euler–Mascheroni constant, and let the sequence wn(a,b,c,d)=∑k...
Let d μ be a probability measure on the unit circle and d ν be the measure formed by adding a pure...
AbstractLet {X,Xn;n⩾1} be a sequence of i.i.d. random variables with EX=0 and EX2=σ2<∞. Set Sn=∑k=1n...
AbstractLet {X,Xn;n⩾1} be a sequence of i.i.d. random variables taking values in a real separable Hi...
AbstractLet X1,X2,… be i.i.d. random variables with partial sums Sn, n⩾1. The now classical Baum–Kat...
AbstractLet {μ(n),n⩾1} be the associated counting process. In this paper, we prove the precise asymp...
AbstractLet X,X1,X2,… be a sequence of nondegenerate i.i.d. random variables with zero means, set Sn...
Given a real number \u3c4, we study the approximation of \u3c4 by signed harmonic sums \u3c3N(\u3c4)...
AbstractLet {Xn,n≥1} be a strictly stationary sequence of random variables and Mn=max{X1,X2,…,Xn}. A...
AbstractThe goal of this paper is to prove the following asymptotic formula Γ(x)≈2πe−b(x+b)xexp(−x−1...
AbstractLet (xjk:j,k=0,1,2,…) be a double sequence of real or complex numbers, and set σmn:=(m+1)−1(...
Given a probability measure μ supported on some compact set K ⊆ C and with orthonormal polynomials {...
AbstractFirst, a maximal inequality for ψ-mixing sequences is given. By using the maximal inequality...
AbstractLet {X,Xn;n⩾1} be a sequence of real-valued i.i.d. random variables with E(X)=0 and E(X2)=1,...
AbstractLet (Xn)n⩾1 be a sequence of real random variables. The local score is Hn=max1⩽i<j⩽n(Xi+⋯+Xj...
AbstractLet γ=0.577215664… denote the Euler–Mascheroni constant, and let the sequence wn(a,b,c,d)=∑k...
Let d μ be a probability measure on the unit circle and d ν be the measure formed by adding a pure...
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