Convergence of Weak*-Scalarly Integrable Functions

Weak Convergence of Random Functions

Let {vij}, i, j = 1, 2, . . . , be i.i.d. symmetric random variables with E(v 11) < ∞, and for each n let Mn = 1 sVnV T n , where Vn = (vij), i = 1, 2, . . . , n, j = 1, 2, . . . , s = s(n), and n/s → y > 0 as n → ∞. Denote by OnΛnO n the spectral decomposition of Mn. Define X ∈ D[0, 1] by Xn(t) = √ n 2 ∑[nt] i=1(y 2 i − 1 n), where (y1, y2, . . . , yn) = O (± 1 √ n ,± 1 √ n , . . . ,± 1 √ n ) ...

On Weak Convergence of Locally Periodic Functions

We have not found proofs of these facts in the literature. The aim of this paper is to present such proofs. Moreover, we show that the first statement also holds for the case p = 1. The two facts described above are used in the proof of the reiterated homogenization result for monotone operators, see [14] and [15]. The solution uξh is used to define a sequence of functions similar to the ones i...

Weak convergence of empirical copula processes indexed by functions

DRAGAN RADULOVIĆ1, MARTEN WEGKAMP2 and YUE ZHAO3 1Department of Mathematics, Florida Atlantic University, 777 Glades Road, Boca Raton, FL 33431, USA. E-mail: [email protected] 2Department of Mathematics and Department of Statistical Science, Cornell University, 432 Malott Hall, Ithaca, NY 14853, USA. E-mail: [email protected] 3Department of Statistical Science, Cornell University, 310 M...

On weak convergence of functionals on smooth random functions ∗

The numbers of level crossings and extremes for random processes and fields play an important role in reliability theory and many engineering applications. In many cases for Gaussian processes the Poisson approximation for their asymptotic distributions is used. This paper extends an approach proposed in Rusakov and Seleznjev (1988) for smooth random processes on a finite interval. It turns out...

The Weak Convergence for Functions of Negatively Associated Random Variables