Almost sure exponential stability of stochastic differential delay equations

This paper is concerned with the almost sure exponential stability of the multidimensional nonlinear stochastic differential delay equation (SDDE) with variable delays of the form dx(t) = f(x(t−δ1(t)), t)dt+g(x(t−δ2(t)), t)dB(t), where δ1, δ2 : R+ → [0, τ ] stand for variable delays. We show that if the corresponding (nondelay) stochastic differential equation (SDE) dy(t) = f(y(t), t)dt + g(y(t), t)dB(t) admits a Lyapunov function (which in particular implies the almost sure exponential stability of the SDE) then there exists a positive number τ ∗ such that the SDDE is also almost sure exponentially stable as long as the delay is bounded by τ ∗ . We provide an implicit lower bound for τ ∗ which can be computed numerically. Moreover, our new theory enables us to design stochastic delay feedback controls in order to stabilize unstable differential equation

The truncated Euler-Maruyama method for stochastic differential delay equations

The numerical solutions of stochastic differential delay equations (SDDEs) under the generalized Khasminskii-type condition were discussed by Mao [15], and the theory there showed that the Euler-Maruyama (EM) numerical solutions converge to the true solutions in probability. However, there is so far no result on the strong convergence (namely in Lp) of the numerical solutions for the SDDEs under this generalized condition. In this paper, we will use the truncated EM method developed by Mao [16] to study the strong convergence of the numerical solutions for the SDDEs under the generalized Khasminskii-type condition

The partially truncated Euler-Maruyama method and its stability and boundedness

The partially truncated Euler–Maruyama (EM) method is proposed in this paper for highly nonlinear stochastic differential equations (SDEs). We will not only establish the finite-time strong Lr-convergence theory for the partially truncated EM method, but also demonstrate the real benefit of the method by showing that the method can preserve the asymptotic stability and boundedness of the underlying SDEs

Surface properties of novel wood-based reinforced composites manufactured from crushed veneers and phenolic resins

This study was performed to determine the surface properties of novel wood-based reinforced composites made from poplar veneers and phenolic resins. The veneers with different thickness (1.8, 4, 6, 8 mm) were finely crushed and then were impregnated with phenolic resins to achieve different resin loading (12, 14, 18%). Finally, they were laminated or random paved to manufacture novel wood-based reinforced composites with different target densities (0.8-1.1 g cm-3). With increased veneer thickness or resin content, the hardness of novel wood-based reinforced composites decreased and their roughness increased. The increase of density contributed to the increased hardness and decreased roughness. The surface wettability of novel wood-based reinforced composites appeared to be closely related to their surface roughness. There was a negative correlation between contact angle and roughness. The novel wood-based reinforced composites prepared by laminated mat formation showed higher hardness, lower roughness than those by random mat formation. Such data of surface properties can be applied to design the novel wood-based reinforced composites products with desired quality and provide basic information for further panel processing

A-optimal design of quadratic random coefficient regression model

A-optimal identical design of quadratic random coefficient regression model on the design domain of [0,1] is constructed in this paper.Loewner order character of A-optimal criterion is proved in the paper and it is proved that A-optimal identical design of quadratic random coefficient regression model could be obtained on three design points including the two extreme settings of the design domain of [0,1].Accurate result of A-optimal identical design of quadratic random coefficient regression model is given in the paper.The result shows that A-optimal identical design of quadratic random coefficient regression model does not depend on the variances of the random effects.The result also shows that the third spectral point of A-optimal design is near the midpoint of the design domain of [0,1] and it's weight coefficient of A-optimal design is near 0.5

D-optimal population designs in linear mixed effects models for multiple longitudinal data

The main purpose of this paper is to investigate D-optimal population designs in multi-response linear mixed models for longitudinal data. Observations of each response variable within subjects are assumed to have a first-order autoregressive structure, possibly with observation error. The equivalence theorems are provided to characterise the D-optimal population designs for the estimation of fixed effects in the model. The semi-Bayesian D-optimal design which is robust against the serial correlation coefficient is also considered. Simulation studies show that the correlation between multi-response variables has tiny effects on the optimal design, while the experimental costs are important factors in the optimal designs

Ridge-type spectral decomposition estimators in mixed effects models with stochastic restrictions

This paper proposes a new estimation of fixed effects in linear mixed models with stochastic restrictions,which is called a conditional ridge-type spectral decomposition estimator.Using the mean squared error matrix and generalized mean squared error as criteria for comparing the estimates,we establish sufficient conditions for the superiority of the conditional ridge-type spectral decomposition estimator over the conditional spectral decomposition estimator.The upper and lower bounds of the relative efficiency are also given.Finally,a simulation example is given to illustrate the theoretical results

Robust Optimum Life-Testing Plans under Progressive Type-I Interval Censoring Schemes with Cost Constraint

This paper considers optimal design problems for the Weibull distribution, which can be used to model symmetrical or asymmetrical data, in the presence of progressive interval censoring in life-testing experiments. Two robust approaches, Bayesian and minimax, are proposed to deal with the dependence of the D-optimality and c-optimality on the unknown model parameters. Meanwhile, the compound design method is applied to ensure a compromise between the precision of estimation of the model parameters and the precision of estimation of the quantiles. Furthermore, to make the design become more practical, the cost constraints are taken into account in constructing the optimal designs. Two algorithms are provided for finding the robust optimal solutions. A simulated example and a real life example are given to illustrate the proposed methods. The sensitivity analysis is also studied. These new design methods can help the engineers to obtain robust optimal designs for the censored life-testing experiments

Bayesian statistical analysis on energy for consumption of large-scale public buildings in shanghai

In the process of measuring the power consumed in buildings,massive quantity of real-time energy consumption data have been accumulated.Salient features of these data include large samples,noise accumulations and the presence of measurement errors,etc.Thus,how to analyze and apply these massive data becomes a very challengeable problem.In this paper,based on the dataset which include the consumption of large-scale public buildings in Shanghai for 2015,we establish a hierarchical Bayesian model to estimate the average monthly consumption and the average annual consumption of large public-scale buildings in 2015.The results will help government regulators to conduct effective evaluation on energy saving for buildings