Convergence rates in the law of logarithm of random elements

1. IntroductionLet {Xu, n 2 1} be a sequence of r.v.IS in the same probability space and put Sa =nZ Xi, n 2 1; L(x) = mad (1, logx).i=1Since the definition of complete convergence is illtroduced by Hsu and Robbins[6], therehave been many authors who devote themselves to the study of the complete convergence forsums of i.i.d. real-valued r.v.'s, and obtain a series of elegys results, see [3,7]. Meanwhile,the convergence rates in the law of logarithm of i.i.d. real-vained r.v.'s have also be…     

强不变原理与完全收敛性的统一形式

本文建立了强不变原理与完全收效性的统一形式，得到了用强不变原理研究完全收敛性的方法，前人许多关于强不交原理和完全收敛性的结论是本文的推论．     

Explicit relation between the solutions of the heat and the Hermite heat equation

There are lots of results on the solutions of the heat equation but much less on those of the Hermite heat equation due to that its coefficients are not constant and even not bounded. In this paper, we find an explicit relation between the solutions of these two equations, thus all known results on the heat equation can be transferred to results on the Hermite heat equation, which should be a completely new idea to study the Hermite equation. Some examples are given to show that known results on the Hermite equation are obtained easily by this method, even improved. There is also a new uniqueness theorem with a very general condition for the Hermite equation, which answers a question in a paper in Proc. Japan Acad. (2005). Supported partially by 973 project (2004CB318000)     

LIL for the Length of the Longest Increasing Subsequences

Let X₁, X₂, ···, X_n, ··· be a sequence of i.i.d. random variables uniformly distributed on [0; 1],and denote by Ln the length of the longest increasing subsequences of X₁, X₂, ···, X_n. Consider the poissonized version?Hn based on Hammersley’s representation in the 2-dimensional space. A law of the iterated logarithm for?Hn is established using the well-known subsequence method and Borel-Cantelli lemma. The key technical ingredient...     

非负张量Z谱的Brauer型上界

In this paper, we have proposed an upper bound for the largest Z-eigenvalue of an irreducible weakly symmetric and nonnegative tensor, which is called the Brauer upper bound:■where■ As applications, a bound on the Z-spectral radius of uniform hypergraphs is presented.     

Structure of subspaces of the compact operators having the Dunford-Pettis property

The structure of the subspaces having the Dunford-Pettis property (DPP) is studied, where is the space of all compact operators on and . The following conditions are shown to be equivalent: (i) M has the DPP, (ii) M is isomorphic to a subspace of (iii) the sets and are relatively compact for all and . The equivalence between (i) and (iii) was recently proven in the case of arbitrary Hilbert spaces by Brown and ülger. It is also shown that (i) and (ii) are equivalent for subspaces . This result is optimal in the sense that for there is a DPP-subspace that fails to be isomorphic to a subspace of . Received January 9, 1998; in final form October 1, 1998     

On the variance of the random sphere of influence graph

We show that the variance of the number of edges in the random sphere of influence graph built on n i.i.d. sites which are uniformly distributed over the unit cube in R ^d, grows linearly with n. This is then used to establish a central limit theorem for the number of edges in the random sphere of influence graph built on a Poisson number of sites. Some related proximity graphs are discussed as well. ©1999 John Wiley & Sons, Inc. Random Struct. Alg., 14, 139–152, 1999     

Estimation of the mean in partially observed branching processes with general immigration

In the paper we investigate asymptotic properties of the branching process with non-stationary immigration which are sufficient for a natural estimator of the offspring mean based on partial observations to be strongly consistent and asymptotically normal. The estimator uses only a binomially distributed subset of the population of each generation. This approach allows us to obtain results without conditions on the criticality of the process which makes possible to develop a unified estimation procedure without knowledge of the range of the offspring mean. These results are to be contrasted with the existing literature related to i.i.d. immigration case where the asymptotic normality depends on the criticality of the process and are new for the fully observed processes as well. Examples of applications in the process with immigration with regularly varying mean and variance and subcritical processes with i.i.d. immigration are also considered.

     

一类三维微分系统正值解的结构(英文)

研究三维微分系统:u′1=a1(t)|u2|λ1sgn u2,u′2=a2(t)|u3|λ2sgn u3,u′3=-a3(t)|u1|λ3sgn u1.假设λi(i=1,2,3)是正的常数,ai(t)(i=1,2,3)在区间[0,∞)上是正的连续函数,根据u的分量ui的特殊渐近条件定义了正值解的几种类型。系统满足条件∫0∞ai(t)dt=∞,i=1,2.     

A stochastic analysis of the NFD bin-packing algorithm

We consider the Next-Fit-Decreasing (NFD) algorithm for the one-dimensional bin packing problem. The input consists of n pieces of i.i.d. sizes. Bounds on the first two moments of the number of bins used in the packing are established for arbitrary size distributions. These bounds are asymptotically tight. For the uniform distribution we also exhibit numerical results and examine their dependence on the support of the size distribution.     

Non parametric estimation of the diffusion coefficient of a diffusion process

This paper deals with the nonparametric estimation of the diffusion coefficient of a diffusion process in the case when it depends only on time. the estimator is based on the regularization of the quadratic mean through multiscale analysis. We then define estimators of the second derivative of the diffusion coefficient, in order to obtain optimal bandwith and to perform a test of linearity. The results we obtain are quite similar to those of the estimation of the density function of an i.i.d. sequence     

基于α-混合序列的学习机器一致收敛速率的界

Vapnik,Cucker和Smale已经证明了,当样本的数目趋于无限时,基于独立同分布序列学习机器的经验风险会一致收敛到它的期望风险.本文把这些基于独立同分布序列的结果推广到了α-混合序列,应用Markov不等式得到了基于α-混合序列的学习机器一致收敛速率的界.     

基于$\alpha$\,-混合序列的学习机器一致收敛速率的界

Vapnik, Cucker和Smale已经证明了, 当样本的数目趋于无限时, 基于独立同分布序列学习机器的经验 风险会一致收敛到它的期望风险\bd 本文把这些基于独立同分布序列的结果推广到了$\alpha$\,-混合序列, 应用Markov不等式得到了基于$\alpha$\,-混合序列的学习机器一致收敛速率的界     

On the pseudo-monotonicity of generalized gradients of nonconvex functions

The paper is devoted to study the class of nonconvex, nondifferentiable functionals on a reflexive Banach space whose generalized Clarke's gradient i s pseudo-monotone i n the sense of Browder-Hess. I n particular, it has been proved that on some restrictions functionals expressed as a pointwise minimum of a finite collection of convex functions belong to this class. Results obtained are used to establish some existence theorems for hemivariational inequalities involving superpotentials under consideration.     

Asymptotic Distribution of the Jump Change-Point Estimator

The asymptotic distribution of the change-point estimator in a jump changepoint model is considered.For the jump change-point model Xi =a + θI{[nTo] ＜ i ≤n} + εi,where εi (i =1,…,n) are independent ide...     

独立指数分布卷积的矩的计算

推导了∑from i=1 to s(λir)/(π j=1 j≠i to s (λi-λj))求和公式,从而解决了独立指数分布卷积的矩的计算.     

On Joint Universality of the Riemann and Hurwitz Zeta-Functions

Mathematical Notes - In 2007, H. Mishou proved the universality theorem on the joint approximation of a pair of analytic functions by the shifts $$(\zeta(s+i\tau),\zeta(s+i\tau,\alpha))$$ of the...     

A note on the law of the iterated logarithm in Hilbert space

Summary Kuelbs (1975) established a Kolmogorov-Erdös-Petrowski type integral test for lower and upper classes in the law of the iterated logarithm for sums of i.i.d. Hilbert space valued Gaussian mean zero random variables. We show that this integral test remains valid for sums of i.i.d. pregaussian mean zero random variables satisfying an additional (very mild) assumption.     

Bifurcation of the Point of Equilibrium in Systems with Zero Roots of the Characteristic Equation

We consider the following real autonomous system of 2d differential equations with a small positive parameter ε: $\dot x_i = x_{i + d} + X_i^{(n + 1)} (x,\varepsilon ), \dot x_{i + d} = - x_i^{2n - 1} + X_{i + d}^{(2n)} (x,\varepsilon ), i = 1,...,d,$ where d≥ 2, n≥2, and the $X_j^{(k)} $ are continuous functions continuously differentiable with respect to x and ε the required number of times in the neighborhood of zero; their expansion begins with order k if we assume that the variables x _i are of first order of smallness, ε is of second order, and the variables x _i+d are of order n. We write out a finite number of explicit conditions on the coefficients of the lower terms in the expansion of the right-hand side of this system guaranteeing that for any sufficiently small ε> 0 the system has one or several d-dimensional invariant tori with infinitely small frequencies of motions on them.     

On the stability of retrial queues

We consider the following Type of problems. Calls arrive at a queue of capacity K (which is called the primary queue), and attempt to get served by a single server. If upon arrival, the queue is full and the server is busy, the new arriving call moves into an infinite capacity orbit, from which it makes new attempts to reach the primary queue, until it finds it non-full (or it finds the server idle). If the queue is not full upon arrival, then the call (customer) waits in line, and will be served according to the FIFO order. If λ is the arrival rate (average number per time unit) of calls and μ is one over the expected service time in the facility, it is well known that μ > λ is not always sufficient for stability. The aim of this paper is to provide general conditions under which it is a sufficient condition. In particular, (i) we derive conditions for Harris ergodicity and obtain bounds for the rate of convergence to the steady state and large deviations results, in the case that the inter-arrival times, retrial times and service times are independent i.i.d. sequences and the retrial times are exponentially distributed; (ii) we establish conditions for strong coupling convergence to a stationary regime when either service times are general stationary ergodic (no independence assumption), and inter-arrival and retrial times are i.i.d. exponentially distributed; or when inter-arrival times are general stationary ergodic, and service and retrial times are i.i.d. exponentially distributed; (iii) we obtain conditions for the existence of uniform exponential bounds of the queue length process under some rather broad conditions on the retrial process. We finally present conditions for boundedness in distribution for the case of nonpatient (or non persistent) customers. This revised version was published online in June 2006 with corrections to the Cover Date.