In this article, we establish a local limit theorem for linear fields of random variables
constructed from iid innovations each with finite second moment. When the coefficients are …

In this paper we study the convergence in distribution and the local limit theorem for the
partial sums of linear random fields with iid innovations that have infinite second moment …

In this paper we investigate the local limit theorem for partial sums of linear sequences of the
form X j=∑ i∈ Z ai ξ j− i. Here (ai) i∈ Z is a sequence of constants satisfying∑ i∈ Z ai 2<∞ …

Let fn be the non-parametric kernel density estimator based on a kernel function K and a
sequence of independent and identically distributed random vectors taking values in R d …

Let (Z n) n≥ 0 be a supercritical Galton–Watson process. The Lotka–Nagaev estimator Z n+
1/Z n is a common estimator for the offspring mean. In this paper, we establish some Cramér …

In this article, we discuss the sharp moderate and large deviations between the quantiles of
population and the quantiles of samples. Cramér type moderate deviations and Bahadur …

Renz [13] has established a rate of convergence 1/n in the central limit theorem for
martingales with some restrictive conditions. In the present paper a modification of the …

Gaussian process regression is widely used to model an unknown function on a continuous
domain by interpolating a discrete set of observed design points. We develop a theoretical …

We first establish a local limit theorem for a linear random field, which is constructed using a
set of real coefficients and a set (referred to as the innovations) of i. id. random variables in L …

n in the central limit theorem for martingales with some restrictive conditions. In the present
paper a modification of the methods, developed by Bolthausen [2] and Grama and Haeusler …