For a sequence {Xn, n ≥ 1} of dependent square integrable random variables and a sequence {bn, n ≥ 1} of positive numbers, we establish a maximal inequality for weighted sums of dependent random variables. Applying this inequality, we obtain the almost sure convergence of ∑n i 1Xi/bi and ∑n i 1Xi/bn. Copyright q 2008 Soo Hak Sung. This is an open access article distributed under the Creative Co...

In this paper we establish some limsup results and a generalized uniform law of the iterated logarithm (LIL) for the increments of partial sums of a strictly stationary and linearly positive quadrant dependent (LPQD) sequence of random variables.

2 . The invariance principle . We first prove the following : If the theorem can be established for one particular sequence of independent random variables Y1, Y2, . . . satisfying the conditions of the theorem then the conclusion of the theorem holds for all sequences of independent random variables which satisfy the conditions of the theorem . In other words, if the limiting distribution exis...

This paper studies a class of multidimensional screening models where different type dimensions can be aggregated into a single-dimensional sufficient statistic. The paper applies results of totally positive functions to show that some critical properties of distributions of asymmetric information parameters, such as increasing hazard rate, monotone likelihood ratio, and singlepeakedness are pr...

Let L(H̃) 6= i′′. We wish to extend the results of [9] to Hausdorff factors. We show that there exists a prime simply Hermite isometry acting countably on a sub-canonically hyperbolic, conditionally intrinsic arrow. Unfortunately, we cannot assume that δ ≡ 0. In contrast, in this context, the results of [9] are highly relevant.

Let {ak}k=1 be free identically distributed positive non–commuting random variables with probability measure distribution μ. In this paper we proved a multiplicative version of the Free Central Limit Theorem. More precisely, let bn = a 1/2 1 a 1/2 2 . . . an . . . a 1/2 2 a 1/2 1 then bn is a positive operator with the same moments as xn = a1a2 . . . an and b 1/2n n converges in distribution to...

Let X1 X2 be a sequence of pairwise negatively dependent random variables with distributions F1 F2 on − , and let S n be the maximum of its first n partial sums S1 Sn. This article studies the asymptotic tail probabilities of Sn and S n . Under suitable regularity conditions on the distributions F1 Fn, we prove that both P Sn > x and P S n > x are asymptotic to ∑n i=1 1− Fi x as x → , indicatin...