一维接触过程的光滑性与稳定性

本文证明了一维接触过程在适当的小扰动下，其极点平稳分布除在临界点λ＿ｃ处外总是光滑的．特别，一维接触过程本身的极点平稳分布关于其参数除在临界点处外总是光滑的．     

Preparation and characterization of mesoporous silica thin films from polyethoxysiloxanes

Tetraethoxysilane (TEOS) and polyethoxysiloxanes (PEOSs; prepared by the acid‐catalyzed hydrolytic polycondensation of TEOS) were subjected to the sol–gel process in the presence of cetyltrimethylammonium bromide (CTAB), respectively. The PEOSs with M_w 700–26,000, as prepared by sol–gel coating of TEOS and PEOS under various conditions, were used. Uniform and crack‐free thin films of thickness 276–613 nm were prepared by spin‐coating of a PEOS solution containing CTAB. When the coating films were sintered at 400 °C, the combustion of ethoxy groups and CTAB took place to provide porous silica thin films. The structure of the thin films was found to be dependent on the molecular weight of PEOS and the molar ratio of CTAB/Si: lamellar or hexagonal phase was observed for M_w less than 15,000 and for CTAB/Si molar ratios greater than 0.10. Honeycomb structures were observed for M_w less than 5000 and for CTAB/Si molar ratios of 0.15. The honeycomb structure was also observed by atomic force microscopy and transmission electron microscope. © 2006 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 44: 2542–2550, 2006     

广义风险过程中渐近方差的非参数估计

本文对广义风险过程中的渐近方差作了非参数估计,得出并证明了两个定理,为广义风险过程中破产概率的区间估计作了理论准备．     

Converging Marriage in Honey-Bees Optimization and Application to Stochastic Dynamic Programming

In this paper, we first refine a recently proposed metaheuristic called “Marriage in Honey-Bees Optimization” (MBO) for solving combinatorial optimization problems with some modifications to formally show that MBO converges to the global optimum value. We then adapt MBO into an algorithm called “Honey-Bees Policy Iteration” (HBPI) for solving infinite horizon-discounted cost stochastic dynamic programming problems and show that HBPI also converges to the optimal value.     

One-dimensional stochastic Burgers equation driven by Lévy processes

In this paper, we proved the global existence and uniqueness of the strong, weak and mild solutions for one-dimensional Burgers equation perturbed by a Poisson form process, a Poisson form and Q-Wiener process with the Dirichlet bounded condition. We also proved the existence of the invariant measure of these models.     

Algorithmic analysis of theMAP/PH/1 retrial queue

In this paper the distribution of the maximum number of customers in a retrial orbit for a single server queue with Markovian arrival process and phase type services is studied. Efficient algorithm for computing the probability distribution and some interesting numerical examples are presented.     

Asymptotic Properties of Quasi-Maximum Likelihood Estimators for ARMA Models with Time-Dependent Coefficients

For about thirty years, time series models with time-dependent coefficients have sometimes been considered as an alternative to models with constant coefficients or non-linear models. Analysis based on models with time-dependent models has long suffered from the absence of an asymptotic theory except in very special cases. The purpose of this paper is to provide such a theory without using a locally stationary spectral representation and time rescaling. We consider autoregressive-moving average (ARMA) models with time-dependent coefficients and a heteroscedastic innovation process. The coefficients and the innovation variance are deterministic functions of time which depend on a finite number of parameters. These parameters are estimated by maximising the Gaussian likelihood function. Deriving conditions for consistency and asymptotic normality and obtaining the asymptotic covariance matrix are done using some assumptions on the functions of time in order to attenuate non-stationarity, mild assumptions for the distribution of the innovations, and also a kind of mixing condition. Theorems from the theory of martingales and mixtingales are used. Some simulation results are given and both theoretical and practical examples are treated. Received 2004; Final version 23 December 2004     

Moments of claims in a Markovian environment

This paper considers discounted aggregate claims when the claim rates and sizes fluctuate according to the state of the risk business. We provide a system of differential equations for the Laplace–Stieltjes transform of the distribution of discounted aggregate claims under this assumption. Using the differential equations, we present the first two moments of discounted aggregate claims in a Markovian environment. We also derive simple expressions for the moments of discounted aggregate claims when the Markovian environment has two states. Numerical examples are illustrated when the claim sizes are specified.     

Two Ergodic Sample-Path Properties of the Poisson Process

For increasing sequences of real numbers we consider two types of asymptotic behavior that remind of the defining property of a (homogeneous) Poisson process according to which the numbers of points in disjoint intervals are independent and follow Poisson distributions with specified parameters. We prove that almost all paths of a Poisson process show this asymptotic behavior, and characterize the Poisson process by these properties. Further we discuss the connection to equidistribution notions.