On the Small Time Asymptotics of Diffusion Processes on Path Groups

In this paper, we obtain the Varadhan type small time asymptotics for diffusion processes on path groups.     

On Characterizations of Proper Efficiency for Nonconvex Multiobjective Optimization

In this paper, nonconvex multiobjective optimization problems are studied. New characterizations of a properly efficient solution in the sense of Geoffrion's are established in terms of the stability of one scalar optimization problem and the existence of an exact penalty function of a scalar constrained program, respectively. One of the characterizations is applied to derive necessary conditions for a properly efficient control-parameter pair of a nonconvex multiobjective discrete optimal control problem with linear constraints.     

Single and Multi-Interval Legendre τ-Methods in Time for Parabolic Equations

In this paper, we take the parabolic equation with periodic boundary conditions as a model to present a spectral method with the Fourier approximation in spatial and single/multi-interval Legendre Petrov–Galerkin method in time. For the single interval spectral method in time, we obtain the optimal error estimate in L ²-norm. For the multi-interval spectral method in time, the L ²-optimal error estimate is valid in spatial. Numerical results show the efficiency of the methods.     

Nonlinear Time Series Analysis Since 1990:Some Personal Reflections

Abstract I reflect upon the development of nonlinear time series analysis since 1990 by focusing on five majorareas of development. These areas include the interface between nonlinear time series analysis and chaos,thenonparametric/semiparametric approach,nonlinear state space modelling,financial time series and nonlinearmodelling of panels of time series.     

首达渗流中关于lim{(N_(on))/n}(n→∞)的一个结果

在二维首达渗流中,设边上通过时间的分布为F（x）,首达时a_（on）的轨道（route）的最短长度为N_（on）,人们猜测存在.本文对F（0）<1/2的情形,就一类特殊的分布证明此猜想成立.     

Exact Buffer Overflow Calculations for Queues via Martingales

Let _n be the first time a queueing process like the queue length or workload exceeds a level n. For the M/M/1 queue length process, the mean _n and the Laplace transform e^-sn is derived in closed form using a martingale introduced in Kella and Whitt (1992). For workload processes and more general systems like MAP/PH/1, we use a Markov additive extension given in Asmussen and Kella (2000) to derive sets of linear equations determining the same quantities. Numerical illustrations are presented in the framework of M/M/1 and MMPP/M/1 with an application to performance evaluation of telecommunication systems with long-range dependent properties in the packet arrival process. Different approximations that are obtained from asymptotic theory are compared with exact numerical results.     

The Flooding Time in Random Graphs

Based on our analysis of the hopcount of the shortest path between two arbitrary nodes in the class G _p (N) of random graphs, the corresponding flooding time is investigated. The flooding time T _N (p) is the minimum time needed to reach all other nodes from one node. We show that, after scaling, the flooding time T _N (p) converges in distribution to the two-fold convolution ^(2*) of the Gumbel distribution function (z)=exp (–e ^–z ), when the link density p _N satisfies Np _N /(log N)³ if N .     

The Law of the Iterated Logarithm for Extreme Waiting Time in Multiphase Queueing Systems

The objective of this research in the queueing theory is the law of the iterated logarithm (LIL) under the conditions of heavy traffic in multiphase queueing systems (MQS). In this paper, the LIL is proved for the extreme values of some important probabilistic characteristics of the MQS, namely, maxima and minima of the summary waiting time of a customer, and maxima and minima of the waiting time of a customer.     

Asymptotic Bound on the Characteristic Function of Signed Linear Serial Rank Statistics

This work establishes an asymptotic bound on the characteristic function of signed linear serial rank statistics. The result is obtained under rather general conditions including the important case of van der Waerden scores. It generalizes the result of Seoh (1983, Ph.D. Thesis, Department of Mathematics, Indiana University) and constitutes an essential step to the elaboration of Berry-Esséen's bounds and the establishment of Edgeworth expansions. These statistics constitute a natural tool for testing the hypothesis of white noise with a symmetrical (unspecified) distribution in comparison to other alternative hypothesis of serial dependence.     

A Regularly Preemptive Model and its Approximations

A regularly preemptive model D,MAP/D ₁,D ₂/1 is studied. Priority customers have constant inter-arrival times and constant service times. On the other hand, ordinary customers' arrivals follow a Markovian Arrival Process (MAP) with constant service times. Although this model can be formulated by using the piecewise Markov process, there remain some difficult problems on numerical calculations. In order to solve these problems, a novel approximation model MAP/MR/1 with Markov renewal services is proposed. These two queueing processes become different due to the existence of idle periods. Thus, a MAP/MR/1 queue with a general boundary condition is introduced. It is a model with the exceptional first service in each busy period. In particular, two special models are studied: one is a warm-up queue and the other is a cool-down queue. It can be proved that the waiting time of ordinary customers for the regular preemption model is stochastically smaller than the waiting time of the former model. On the other hand, it is stochastically larger than the waiting time of the latter model.