Cluster Sets of Self-Normalized Sums

We determine the cluster sets of certain self-normalized sums of i.i.d. random variables. In the process, we obtain a refined large deviation result for sums in the domain of attraction of a stable law.     

Large deviations for sums of i.i.d. random compact sets

We prove a large deviation principle for Minkowski sums of i.i.d. random compact sets in a Banach space, that is, the analog of Cramér theorem for random compact sets.

     

A large deviation principle for bootstrapped sample means

A large deviation principle for bootstrapped sample means is established. It relies on the Bolthausen large deviation principle for sums of i.i.d. Banach space valued random variables. The rate function of the large deviation principle for bootstrapped sample means is the same as the classical one.

     

一个复合风险模型的引入及其大偏差估计的建立

本文研究了关于独立随机和精大偏差的估计问题,改进了文献[4,7]的结果。首先我们引入了一个比过去工作更现实复合更新风险模型,然后在该模型下建立了与文献中完全相同的精大偏差结果。     

上尾渐近独立随机变量和的大偏差的渐近下界(英文)

本文研究了多元风险模型中服从长尾分布的带上尾渐近独立的随机变量和的大偏差渐近下界.利用大偏差的经典求法,得到了随机变量的非随机和和随机和的大偏差表达式,推广了独立同分布情形下的相关结论.     

Small deviation probabilities of weighted sums under minimal moment assumptions

We examine small deviation probabilities of weighted sums of i.i.d.r.v. with a power decay at zero under moment assumptions close to necessary.     

The cluster index of regularly varying sequences with applications to limit theory for functions of multivariate Markov chains

We introduce the cluster index of a multivariate stationary sequence and characterize the index in terms of the spectral tail process. This index plays a major role in limit theory for partial sums of sequences. We illustrate the use of the cluster index by characterizing infinite variance stable limit distributions and precise large deviation results for sums of multivariate functions acting on a stationary Markov chain under a drift condition.     

L族END的多元部分和的精确大偏差下界

从保险的实际出发,研究服从长尾分布族(L族)上的多元风险模型中随机变量序列的部分和的精确大偏差,其中假设随机变量序列是一列延拓负相依(END)的、同分布的随机变量序列,利用基于求L族的精确大偏差的方法得到了随机变量部分和的渐近下界.     

Large deviations for sums indexed by the generations of a Galton–Watson process

In this paper, we study the large deviation behavior of sums of i.i.d. random variables X _i , where Z _n is the nth generation of a supercritical Galton–Watson process. We assume the finiteness of the moments and EZ ₁ logZ ₁ . The underlying interplay of large deviation probabilities of partial sums of the X _i and of lower deviation probabilities of Z is clarified. Here, we heavily use lower deviation probability results on Z we recently published in [7]. This paper has been written during the time the second author was a staff member of the WIAS Berlin.     

Eigenvalue Distributions and Geometry of Banach Spaces

We consider the sums Z⁽ⁿ⁾ of i.i.d. random vectors taking values in a d-dimensional Euclidean space. It is assumed that the so-called CRAMER condition holds in a neighbourhood of the origin. We establish lower bounds for the large deviation probabilities P(Z⁽ⁿ⁾ ? A) with A belonging to a large class of sets.