This paper studies estimation of a partially specified spatial autoregressive model with heteroskedasticity error term. Under the assumption of exogenous regressors and exogenous spatial weighting matrix, the unknown parameter is estimated by applying the instrumental variable estimation. Under certain sufficient conditions, the proposed estimator for the finite dimensional parameters is shown to be root-n consistent and asymptotically normally distributed; The proposed estimator for the unknown function is shown to be consistent and asymptotically distributed as well, though at a rate slower than root-n. Consistent estimators for the asymptotic variance-covariance matrices of both estimators are provided. Monte Carlo simulations suggest that the proposed procedure has some practical value.
In this paper, we will show that under some smallness conditions, the planar diffusion wave v(x_{1}/√1+t) is stable for a quasilinear wave equation with nonlinear damping: v_{tt} - Δf(v) + v_{t} + g(v_{t}) = 0, x = (x_{1}, x_{2}, … , x_{n}) ∈ R^{n}, where v(x_{1}/√1+t) is the unique similar solution to the one dimensional nonlinear heat equa- tion: v_{t} - f(v)_{x1x1} = 0, f'(v) > 0, v(±∞, t) = v_{±}, v_{+}≠v_{-}. We also obtain the L^{∞} time decay rate which reads ||v-v|| _{L∞}= O(1)(1 + t)^{-r/4} , where r = min{3, n}. To get the main result, the energy method and a new inequality have been used.
This article deals with the Riemann-Hilbert boundary value problem for quasilinear mixed (elliptichyperbolic) complex equations of first order with degenerate rank 0. Firstly, we give the representation theorem and prove the uniqueness of solutions for the boundary value problem. Afterwards, by using the method of successive iteration, the existence and estimates of solutions for the boundary value problem are verified. The above problem possesses the important applications to the Tricomi problem of mixed type equations of second order. In this article, the proof of Hölder continuity of a singular double integer is very difficult and interesting as in this Section 4 below.
In this paper, we consider a discrete-time preemptive priority queue with different service completion probabilities for two classes of customers, one with high-priority and the other with low-priority. This model corresponds to the classical preemptive priority queueing system with two classes of independent Poisson customers and a single exponential server. Due to the possibility of customers' arriving and departing at the same time in a discrete-time queue, the model considered in this paper is more complicated than the continuous- time model. In this model, we focus on the characterization of the exact tail asymptotics for the joint stationary distribution of the queue length of the two types of customers, for the two boundary distributions and for the two marginal distributions, respectively. By using generating functions and the kernel method, we get the exact tail asymptotic properties along the direction of the low-priority queue, as well as along the direction of the high-priority queue.
In this paper, we'll prove new representation theorems for a kind of second order stochastic integral-differential operator by stochastic differential equations (SDEs) and backward stochastic differential equations (BSDEs) with jumps, and give some applications.
The construction of confidence intervals for quantiles of a population under a associated sample is studied by using the blockwise technique. It is shown that the blockwise empirical likelihood (EL) ratio statistic is asymptotically χ^{2}-type distributed, which is used to obtain EL-based confidence intervals for quantiles of a population.
We propose a new expected value of rooted graph in this article,that is, when G is a rooted graph that each vertex may independently succeed with probability p when catastrophic thing happened, we consider the expected number of edges in the operational component of G which containing the root. And we get a very important and useful compute formula which is called deletion-contraction edge formula. By using this formula, we get the computational formulas of expected value for some special graphs. We also discuss the mean of expected value when parameter p has certain prior distribution. Finally, we propose mean-variance optimality when rooted graph has the equilibrium point which has larger mean and smaller variance.
Feedback stabilization for a class of second order singular distributed parameter system with multi-inputs is discussed via functional analysis and operator theory in Hilbert space, the solutions of the problem and the constructive expressions of the solutions are given by the generalized inverse of bounded linear operator. This research is theoretically important for studying the stability of the singular distributed parameter system.
The equity-indexed annuity (EIA) contract offers a proportional participation in the performance of a specified equity index, in addition to a guaranteed return on the single premium. How to manage the risk of the EIA is an important issue. This paper considers the hedging of the EIA. We assume that the parameters of the financial model depend on a continuous-time finite-state Markov chain and the Markov chain is observed, that is the Markov regime switching model. The state of the Markov chain can be interpreted as the state of an economy. Under the regime switching model, we obtain the risk-minimizing hedging strategy for the EIA.
A uniqueness theorem of a solution of a system of nonlinear equations is given. Using this result uniqueness theorems for power orthogonal polynomials, for a Gaussian quadrature formula of an extended Chebyshev system, and for a Gaussian Birkhoff quadrature formula are easily deduced.
Let B_{Ω}^{p}, 1 ≤ p ≤ ∞, be the set of all bounded functions in L^{p}(R) which can be extended to entire functions of exponential type Ω. The uniform bounds for truncation error of Shannon sampling expansion from local averages are obtained for functions f ∈ B_{Ω}^{p} with the decay condition
|f(t)|≤A/|t|^{δ}, t≠0,where A and δ are positive constants. Furthermore we also establish similar results for non-bandlimit functions in Besov classes with the same decay condition as above.
In this paper, we first study a property about the generator g of Backward Stochastic Differential Equation (BSDE) when the price of contingent claims can be represented by a multidimensional BSDE in the no-arbitrage financial market. Furthermore, motivated by the behavior of agents in finance market, we introduce a new total order on R^{n} and obtain a necessary and sufficient condition for comparison theorem of multidimensional BSDEs under this order. We also give some further results for .
The varying-coefficient partially linear regression model is proposed by combining nonparametric and varying-coefficient regression procedures. Wong, et al. (2008) proposed the model and gave its estimation by the local linear method. In this paper its inference is addressed. Based on these estimates, the generalized like- lihood ratio test is established. Under the null hypotheses the normalized test statistic follows a χ^{2}-distribution asymptotically, with the scale constant and the degrees of freedom being independent of the nuisance param- eters. This is the Wilks phenomenon. Furthermore its asymptotic power is also derived, which achieves the optimal rate of convergence for nonparametric hypotheses testing. A simulation and a real example are used to evaluate the performances of the testing procedures empirically.
In this paper, we study the existence of multiple solutions to the following nonlinear elliptic boundary value problem of p-Laplacian type:
(*)
where 1 < p < ∞, Ω⊆R^{N} is a bounded smooth domain, Δ_{pu} = div (|Du|^{p-2}Du) is the p-Laplacian of u and f: Ω× R→R satisfies = l uniformly with respect to x∈Ω, and l is not an eigenvalue of Δ_{p} in W_{0}^{1,p} (Ω) but f(x, t) dose not satisfy the Ambrosetti-Rabinowitz condition. Under suitable assumptions on f(x, t), we have proved that (*) has at least four nontrivitial solutions in W_{0}^{1,p} (Ω) by using Nonsmooth Mountain-Pass Theorem under (C)_{c} condition. Our main result generalizes a result by N. S. Papageorgiou, E. M. Rocha and V. Staicu in 2008 (Calculus of Variations and Partial Differential Equations, 33: 199-230(2008)) and a result by G. B. Li and H. S. Zhou in 2002 (Journal of the London Mathematical Society, 65: 123-138(2002)).
A recursive formula of the Gerber-Shiu discounted penalty function for a compound binomial risk model with by-claims is obtained. In the discount-free case, an explicit formula is given. Utilizing such an explicit expression, we derive some useful insurance quantities, including the ruin probability, the density of the deficit at ruin, the joint density of the surplus immediately before ruin and the deficit at ruin, and the density of the claim causing ruin.
The viscous contact wave for the compressible Navier-Stokes equations has recently been shown to be asymptotically stable provided that all the L_{2} norms of initial perturbations, their derivatives and/or anti-derivatives are small. The main purpose of this paper is to study the asymptotic stability and convergence rate of the viscous contact wave with a large initial perturbation. For this purpose, we introduce a positive number l in the construction of a smooth approximation of the contact discontinuity for the compressible Euler equations and then we make the quantity l to be sufficiently large in order to control the growth induced by the nonlinearity of the system and the interaction of waves from different families. This makes for us to estimate the L_{2} norms of the solution and its derivative for perturbation system without assuming that L_{2} norms of the anti-derivatives and the derivatives of initial perturbations are small.
Numerical solution of the parabolic partial differential equations with an unknown parameter play a very important role in engineering applications. In this study we present a high order scheme for determining unknown control parameter and unknown solution of two-dimensional parabolic inverse problem with overspe- cialization at a point in the spatial domain. In this approach, a compact fourth-order scheme is used to discretize spatial derivatives of equation and reduces the problem to a system of ordinary differential equations (ODEs). Then we apply a fourth order boundary value method to the solution of resulting system of ODEs. So the proposed method has fourth order of accuracy in both space and time components and is unconditionally stable due to the favorable stability property of boundary value methods. The results of numerical experiments are presented and some comparisons are made with several well-known finite difference schemes in the literature. Also we will investigate the effect of noise in data on the approximate solutions.
In this article we investigate the uniformity of direct union of k copies of Chord which is an improved version of Chord P2P system. We are interested in the maximal and the minimal areas controlled by nodes in the system. We recall that the function nn^{-2} is a threshold for a number of nodes in Chord controlling small areas. In this paper we show that the function n ^{k}√k! ·n^{-(1+ 1/k)} is a lower threshold and that the function n(1/n)ln(nln^{k-1}(n(k-1)!)/(k-1)!) is an upper threshold for sizes of areas controlled by nodes in the direct union of k copies of Chord.
A new nonlinear predator-prey model with incomplete trophic transfer is introduced. In this model, we assume that the rate of the trophic absorption of the predator is less than the rate of the conversion of consumed prey to predator in the Ivlev-type functional responses. The existence and uniqueness of the positive equilibrium of the model and the stability of the equilibrium of the model are studied under various conditions. Hopf bifurcation analysis of the delayed model is provided.
Low rank matrix recovery is a new topic drawing the attention of many researchers which addresses the problem of recovering an unknown low rank matrix from few linear measurements. The matrix Dantzig selector and the matrix Lasso are two important algorithms based on nuclear norm minimization. In this paper, we first prove some decay properties of restricted isometry constants, then we discuss the recovery errors of these two algorithms and give a new bound of restricted isometry constant to guarantee stable recovery, which improves the results of [11].
We consider the boundary value problem Δu + |x|^{2α} |u|^{p-1}u = 0, -1 < α ≠ 0, in the unit ball B with the homogeneous Dirichlet boundary condition, when p is a large exponent. By a constructive way, we prove that for any positive integer m, there exists a multi-peak nodal solution u_{p} whose maxima and minima are located alternately near the origin and the other m points = (λcos(2π(l-1)/m), λ sin(2π(l-1)/m), l = 2, … ,m+ 1, such that as p goes to +∞,
p|x|^{2α}|μ_{p}|^{p-1}μ_{p}→8πe(1 + α)δ_{0} +, where λ ∈ (0, 1), m is an odd number with (1+α)(m+2)-1 > 0, or m is an even number. The same techniques lead also to a more general result on general domains.
In this paper, we study the existence of multiple solutions for the following quasilinear elliptic system:
Multiplicity of solutions for the quasilinear problem is obtained via variational method.