The Asymptotic Distribution of Trimmed Sums

The Asymptotic Distribution of Exponential Sums, I

On the Asymptotic Distribution of Certain Sums

The asymptotic distribution of randomly weighted sums and self - normalized sums ∗

We consider the self-normalized sums Tn = ∑n i=1 XiYi/ ∑n i=1 Yi, where {Yi : i ≥ 1} are non-negative i.i.d. random variables, and {Xi : i ≥ 1} are i.i.d. random variables, independent of {Yi : i ≥ 1}. The main result of the paper is that each subsequential limit law of Tn is continuous for any non-degenerate X1 with finite expectation, if and only if Y1 is in the centered Feller class.

Asymptotic distribution of eigenvalues of the elliptic operator system

Since the theory of spectral properties of non-self-accession differential operators on Sobolev spaces is an important field in mathematics, therefore, different techniques are used to study them. In this paper, two types of non-self-accession differential operators on Sobolev spaces are considered and their spectral properties are investigated with two different and new techniques.

On the Central Limit Theorem for Modulus Trimmed Sums

We prove a functional central limit theorem for modulus trimmed i.i.d. variables in the domain of attraction of a nonnormal stable law. In contrast to the corresponding result under ordinary trimming, our CLT contains a random centering factor which is inevitable in the nonsymmetric case. The proof is based on the weak convergence of a two-parameter process where one of the parameters is time a...