Estimating tail probabilities of heavy tailed distributions with asymptotically zero relative error

Efficient estimation of tail probabilities involving heavy tailed random variables is amongst the most challenging problems in Monte-Carlo simulation. In the last few years, applied probabilists have achieved considerable success in developing efficient algorithms for some such simple but fundamental tail probabilities. Usually, unbiased importance sampling estimators of such tail probabilities are developed and it is proved that these estimators are asymptotically efficient or even possess the desirable bounded relative error property. In this paper, as an illustration, we consider a simple tail probability involving geometric sums of heavy tailed random variables. This is useful in estimating the probability of large delays in M/G/1 queues. In this setting we develop an unbiased estimator whose relative error decreases to zero asymptotically. The key idea is to decompose the probability of interest into a known dominant component and an unknown small component. Simulation then focuses on estimating the latter ‘residual’ probability. Here we show that the existing conditioning methods or importance sampling methods are not effective in estimating the residual probability while an appropriate combination of the two estimates it with bounded relative error. As a further illustration of the proposed ideas, we apply them to develop an estimator for the probability of large delays in stochastic activity networks that has an asymptotically zero relative error.      

Two-sided bounds for the distribution of the deficit at ruin in the renewal risk model

We obtain lower and upper bounds for the severity of ruin in the renewal (Sparre Andersen) model of risk theory. We present two types of bounds: (i) bounds applicable generally; and (ii) exponential bounds for the case where the adjustment coefficient of the risk process exists. Many of these bounds are obtained using existing bounds and the integral equation for the severity of ruin.     

Lower bounds for transition probabilities on graphs

The paper presents two results. The first one provides separate conditions for the upper and lower estimates of the distribution of the time of exit from balls of a random walk on a weighted graph. The main result of the paper is that the lower estimate follows from the elliptic Harnack inequality. The second result is an off-diagonal lower bound for the transition probability of the random walk.     

双对数模型对模型模拟误差的放缩问题探讨

对双对数模型lg Y=a0+a1lg X1+a2lg X2+…+anlg Xn与其对应的指数模型y=c0xa11xa22…xann的模拟相对误差的关系进行了探讨,指出双对数模型具有放大和缩小指数模型相对误差的特性.对二者的关系进行了理论推导和实例验证,并给出了二者的定量关系式.     

Error estimate for the approximation of nonlinear conservation laws on bounded domains by the finite volume method

In this paper we derive a priori and a posteriori error estimates for cell centered finite volume approximations of nonlinear conservation laws on polygonal bounded domains. Numerical experiments show the applicability of the a posteriori result for the derivation of local adaptive solution strategies.

     

万用表检测电容器方法分析及改进

本文从教学实验的实践出发,对使用万用表测量电容器容量的方法进行了分析,并对电路进行了一定改进。     

CDMA时变色散信道的两级盲辨识算法

本文通过对时变信道的扩展函数在时频域进行正则采样，得到了CDMA时变系统的离散正则模型。针对该模型提出了一种具有较低运算量的两级盲辨识算法。为避免两级算法产生的误差传播效应，文章将理想SIMO模型等效为加性噪声模型来处理。与基展开模型方法相比，该算法具有不需利用观测数据的高阶统计量估计展开基频率的优点。文章通过仿真验证了该算法是可行的。     

On the covariance of the level sizes in random recursive trees

In this paper we study the covariance structure of the number of nodes k and l steps away from the root in random recursive trees. We give an analytic expression valid for all k, l and tree sizes N. The fraction of nodes k steps away from the root is a random probability distribution in k. The expression for the covariances allows us to show that the total variation distance between this (random) probability distribution and its mean converges in probability to zero. © 2002 Wiley Periodicals, Inc. Random Struct. Alg., 20: 519–539, 2002