arXiv subjects
Publications and source records attributed to Lingtao Kong.
Operator self-similar processes, as an extension of self-similar processes, have been studied extensively. In this work, we study limit theorems for functionals of Gaussian vectors. Under some conditions, we determine that the limit of partial sums of functionals of a stationary Gaussian sequence of random vectors is an operator self-similar process
In Liu and Lin (Statist. Probab. Letters, 2006), they introduced a kind of complete moment convergence which includes complete convergence as a special case. Inspired by the study of complete convergence, in this paper, we study the convergence rates of the precise asymptotics for this kind of complete moment convergence and get the corresponding convergence rates.
Let $\{X_n,n\geq 1\}$ be a sequence of i.i.d. random variables with partial sums $\{S_n,n\geq 1\}$. Based on the classical Baum-Katz theorem, a paper by Heyde in 1975 initiated the precise asymptotics for the sum $\sum_{n\geq 1}\mbox{P}(|S_n|\geqεn)$ as $ε$ goes to zero. Later, Klesov determined the convergence rate in Heyde's theorem. The aim of this paper is to extend Klesov's result to the precise asymptotics for Davis law of large numbers, a theorem in Gut and Spătaru [2000a].