一类随机游动上确界的密度的渐近性

Kluppelberg^[1], Asmussen 等^[2] 研究了增量有有限负均值的随机游动上确界的密度的渐近性. 该文则在 Denisov 等^[3], 程东亚和王岳宝^[4]的基础上, 进一步研究了增量均值为负无穷的随机游动上确界的密度的渐近性. 最后, 为了说明常见重尾分布大多满足上述结果的条件, 该文给出了一些分布族的性质.     

Asymptotic Poisson Character of Extremes in Non-Stationary Gaussian Models

Let X be a non-stationary Gaussian process, asymptotically centered with constant variance. Let u be a positive real. Define R_u(t) as the number of upcrossings of level u by the process X on the interval (0, t]. Under some conditions we prove that the sequence of point processes (R_u)_u>0 converges weakly, after normalization, to a standard Poisson process as u tends to infinity. In consequence of this study we obtain the weak convergence of the normalized supremum to a Gumbel distribution.AMS 2000 Subject Classifications Primary—60G70, 60G15     

Orthogonal partitions in designed experiments

A survey is given of the statistical theory of orthogonal partitions on a finite set. Orthogonality, closure under suprema, and one trivial partition give an orthogonal decomposition of the corresponding vector space into subspaces indexed by the partitions. These conditions plus uniformity, closure under infima and the other trivial partition give association schemes. Examples covered by the theory include Latin squares, orthogonal arrays, semilattices of subgroups, and partitions defined by the ancestral subsets of a partially ordered set (the poset block structures).Isomorphism, equivalence and duality are discussed, and the automorphism groups given in some cases. Finally, the ideas are illustrated by some examples of real experiments.Dedicated to Hanfried Lenz on the occasion of his 80th birthday.     

Impulsive efects on global stability of models based on impulsive diferential equations with “supremum” and variable impulsive perturbations

Sufcient conditions are investigated for the global stability of the solutions to models based on nonlinear impulsive diferential equations with "supremum" and variable impulsive perturbations. The main tools are the Lyapunov functions and Razumikhin technique. Two illustrative examples are given to demonstrate the efectiveness of the obtained results.     

On a quadratic integral equation with supremum involving Erdélyi‐Kober fractional order

We introduce Erdélyi‐Kober fractional quadratic integral equation with supremum, namely . This equation contains as special cases numerous integral equations studied by other authors. We show that there exists at least one monotonic solution belonging to C[0, 1] of our equation. The main tools in our analysis are Darbo fixed point theorem and the measure of noncompactness related to monotonicity which was introduced by Bana? and Olszowy. Finally, we present an example for illustrating the natural realizations of our abstract results.     

多指标独立随机变量的重对数律及其应用

对于多指标独立同分布的随机变量序列,在某些更广泛的正则化序列下,本文给出了重对数律成立的充分必要条件.作为应用,本文讨论了正则和极大值函数的矩存在的充分必要条件.     

Ruin Theory for the Risk Process Described by PDMPs

In this paper we consider the risk process that is described by a piecewise deterministic Markov processes(PDMP).We first present the construction of the risk process and them discuss some ruin problems for this new kind of risk model.     

An Extremal Limit Theorem for the Argmax Process of Brownian Motion Minus a Parabolic Drift

We study the extremal behavior of the stationary processes and , on increasing intervals [0,T], as , where V(t) is the location of the maximum of standard two-sided Brownian motion minus a parabolic drift. The result can be applied to the asymptotic behavior of the -risk of several nonparametric maximum likelihood estimators.     

无平方因子阶群的自同构群阶的上确界

群阶为素数方幂（即ｐ－ 群）时已得到该群自同构群阶的上确界,而对于其他情形的群,同样的问题要复杂得多． 本文在群阶无平方因子且为偶数时,给出了这类群的自同构群阶的上确界．     

Ten penalisation results of Brownian motion involving its one-sided supremum until first and last passage times, VIII

We penalise Brownian motion by a function of its one-sided supremum considered up to the last zero before t, respectively first zero after t, of that Brownian motion. This study presents some analogy with penalisation by the longest length of Brownian excursions, up to time t.