In this paper, the estimation of variance components in the linear mixed model with two random effects is investigated. The class of combination estimates based on the quadratic invariant statistics and consistent nonnegative estimates are obtained. Furthermore, it is shown that the consistent nonnegative estimate dominates ANOVA estimate under some conditions.
This paper addresses the simultaneous determination of pricing and inventory replenishment strategies under a fluctuating environment. Specifically, we analyze the single item, periodic review model. The demand consists of two parts: the deterministic component, which is influenced by the price, and the stochastic component (perturbation). The distribution of the stochastic component is determined by the current state of an exogenous Markov chain. The price that is charged in any given period can be specified dynamically. A replenishment order may be placed at the beginning of some or all of the periods, and stockouts are fully backlogged. Ordering costs that are lower semicontinuous, and inventory/backlog (or surplus) costs that are continuous with polynomial growth. Finite-horizon and infinite-horizon problems are addressed. Existence of optimal policies is established. Furthermore, optimality of (s,S,p)-type policies is proved when the ordering cost consists of fixed and proportional cost components and the surplus cost (these costs are all state-dependent) is convex.
In this paper, three numerical schemes with high accuracy for the coupled Schrödinger equations are studied. The conservative properties of the schemes are obtained and the plane wave solution is analysised. The split step Runge-Kutta scheme is conditionally stable by linearized analyzed. The split step compact scheme and the split step spectral method are unconditionally stable. The trunction error of the schemes are discussed. The fusion of two solitions colliding with different β is shown in the figures. The numerical experments demonstrate that our algorithms are effective and reliable.
In this paper, the linear stability of symplectic methods for Hamiltonian systems is studied. In particular, three classes of symplectic methods are considered: symplectic Runge-Kutta (SRK) methods, symplectic partitioned Runge-Kutta (SPRK) methods and the composition methods based on SRK or SPRK methods. It is shown that the SRK methods and their compositions preserve the ellipticity of equilibrium points unconditionally, whereas the SPRK methods and their compositions have some restrictions on the time-step.
This paper proposes some regularity conditions, which result in the existence, strong consistency and asymptotic normality of maximum quasi-likelihood estimator (MQLE) in quasi-likelihood nonlinear models (QLNM) with random regressors. The asymptotic results of generalized linear models (GLM) with random regressors are generalized to QLNM with random regressors.
This paper deals with the output feedback H∞ control problem for a class of nonlinear stochastic systems. Based on the latest developed theory of stochastic dissipation, a notable result about the nonlinear H∞ output feedback control of deterministic system is generalized to the stochastic case. Finally, in the cases of state feedback and output feedback, two families of controllers are provided respectively.
The singularly perturbed boundary value problem of scalar integro-differential equations has been studied extensively by the differential inequality method . However, it does not seem possible to carry this method over to a corresponding nonlinear vector integro-differential equation. Therefore , for n-dimensional vector integro-differential equations the problem has not been solved fully. Here, we study this nonlinear vector problem and obtain some results. The approach in this paper is to transform the appropriate integro-differential equations into a canonical or diagonalized system of two first-order equations.
By constructing auxiliary differential equations, we obtain peaked solitary wave solutions of the generalized Camassa-Holm equation, including periodic cusp waves expressed in terms of elliptic functions.
The exact parametric representations of the traveling wave solutions for a nonlinear elastic rod equation are considered. By using the method of planar dynamical systems, in di?erent parameter regions, the phase portraits of the corresponding traveling wave system are given. Exact explicit kink wave solutions, periodic wave solutions and some unbounded wave solutions are obtained.
In this paper, we establish some new generalized KKM-type theorems based on weakly generalized KKM mapping without any convexity structure in topological spaces. As applications, some minimax inequalities and an existence theorem of equilibrium points for an abstract generalized vector equilibrium problem are proved in topological spaces. The results presented in this paper unify and generalize some known results in recent literature.
The changes of numeraire can be used as a very powerful mean in pricing contingent claims in the context of a complete market. We apply the method of nurmeraire changes to evaluate convertible bonds when the instantaneous growth and variance of the value of issuer and those of zero-coupon bonds follow a general adapted stochastic process in this paper. A closed-form solution is derived when the instantaneous growth and variance of the value of issuer and those of zero-coupon bonds are deterministic function of time. We also consider a special case when the asset price follows GBM (Geometric Brownian Motion) and interest rate follows Vasicek’s model.
In this paper we study reflected and doubly reflected backward stochastic differential equations (BSDEs, for short) driven by Teugels martingales associated with Lévy process satisfying some moment conditions and by an independent Brownian motion. For BSDEs with one reflecting barrier, we obtain a comparison theorem using the Tanaka-Meyer formula. For BSDEs with two reflecting barriers, we first prove the existence and uniqueness of the solutions under the Mokobodski’s condition by using the Snell envelope theory and then we obtain a comparison result.
This paper considers a class of delayed renewal risk processes with a threshold dividend strategy. The main result is an expression of the Gerber-Shiu expected discounted penalty function in the delayed renewal risk model in terms of the corresponding Gerber-Shiu function in the ordinary renewal model. Subsequently, this relationship is considered in more detail in both the stationary renewal risk model and the ruin probability.