ASYMPTOTIC ESTIMatION OF ROBIN BOUNDARY VALUE PROBLEM FOR THIRD NONLINEAR EQUATION

In this paper, we study Robin boundary vlaue problem for third order equation εx'' = f(t, x, x', ω(ε)x', ε), x(0) = A, a1x'(0) - a2x'(0) = B, b1x'(1) +b2x'(1) = C. By means of upper and lower solutions method, and the existenceand asymptotic estimation of solution are established.

Asymptotic behavior of Mean-CVaR portfolio selection model under nonparametric framework

Portfolio selection is an important issue in finance and it involves the balance between risk and return. This paper investigates portfolio selection under Mean-CVa R model in a nonparametric framework with α-mixing data as financial data tends to be dependent. Many works have provided some insight into the performance of portfolio selection from the aspects of data and simulation while in this paper we concentrate on the asymptotic behaviors of the optimal solutions and risk estimation in theory.

具有勢壘的Sturm-Liouville算子的特徵值和特徵函數

We aim to find the eigenvalues and eigenfunctions of the barrier potential case for Strum-Liouville operator on the finite interval [0,π] when λ > 0. Generally, the eigenvalue problem for the Sturm-Liouville operator is often solved by using integral equations, which are sometimes complex to solve, and difficulties may arise in computing the boundary values. Considering the said complexity, we have successfully developed a technique to give the asymptotic formulae of the eigenvalue and the eigenfunction for Sturm-Liouville operator with barrier potential. The results are of significant interest in the field of quantum mechanics and atomic systems to observe discrete energy levels.

NON-NEWTON FILTRATION EQUATION WITH SPECIAL MEDIUM VOID

This paper considers the existence and asymptotic estimates of global solutions and finite time blowup of local solution of non-Newton filtration equation with special medium void of the following form:where , ft is a smooth bounded domain in RN(N≥3), 0∈Ω, The result of asymptotic estimate of global solution depends on the best constant in Hardy inequality.

THIRD-ORDER NONLINEAR SINGULARLY PERTURBED BOUNDARY VALUE PROBLEM

Third order singulary perturbed boundary value problem by means of differential inequality theories is studied. Based on the given results of second order nonlinear boundary value problem, the upper and lower solutions method of third order nonlinear boundary value problems by making use of Volterra type integral operator was established. Specific upper and lower solutions were constructed, and existence and asymptotic estimates of solutions under suitable conditions were obtained. The result shows that it seems to be new to apply these techniques to solving these kinds of third order singularly perturbed boundary value problem. An example is given to demonstrate the applications.

SINGULAR PERTURBATION OF BOUNDARY VALUE PROBLEMS FOR SECOND ORDER NONLINEAR ORDINARY DIFFERENTIAL EQUATIONS ON INFINITE INTERVAL(Ⅱ)

In this paper the existence of solutions of the singularly perturbed boundary value problems on infinite interval for the second order nonlinear equation containing a small parameteris examined, where are constants, and i=0,1 . Moreover, asymptotic estimates of the solutions for the above problems are given.

薄膜外延生长的四阶抛物模型解的渐近性质

This paper deals with a homogeneous Neumann initial-boundary problem of a 4th-order parabolic equation modeling epitaxial growth of thin film. We determine the classification of initial energy on the existence of blow-up, global existence and extinction of solutions by using the potential well method and the auxiliary function method.Moreover, asymptotic estimates on global solution and extinction solution are studied,respectively.

Sieve MLE for Generalized Partial Linear Models with Type Ⅱ Interval-censored Data

This article concerded with a semiparametric generalized partial linear model （GPLM） with the type Ⅱ censored data. A sieve maximum likelihood estimator （MLE） is proposed to estimate the parameter component, allowing exploration of the nonlinear relationship between a certain covariate and the response function. Asymptotic properties of the proposed sieve MLEs are discussed. Under some mild conditions, the estimators are shown to be strongly consistent. Moreover, the estimators of the unknown parameters are asymptotically normal and efficient, and the estimator of the nonparametric function has an optimal convergence rate.

ON ASYMPTOTICALLY EFFICIENT ESTIMATION FOR A SEMIPARAMETRIC REGRESSION MODEL

Consider the model Y=Xτβ+g(T)+ε. Here g is a smooth but unknown function, β is a k×1 parameter vector to be estimated and ε, is an random error with mean 0 and variance σ2. The asymptotically efficient estimator of β is constructed on the basis of the model Yi=Xτiβ+g(Ti)+εi, i=1,…,n, when the density functions of (X,T) and ε are known or unknown.Finally, an asymptotically normal estimator of σ2 is given.

Asymptotics for Certain Harmonic Functions and the Martin Compactification on the Quaternionic Heisenberg Group

In this paper, we make the asymptotic estimates of the heat kernel for the quaternionic Heisenberg group in various cases. We also use these results to deduce the asymptotic estimates of certain harmonic functions on the quaternionic Heisenberg group. Moreover a Martin compactification of the quaternionic Heisenberg group is constructed, and we prove that the Martin boundary of this group is homeomorphic to the unit ball in the quaternionic field.

On the Asymptotic Behavior of Nearest Neighbor Estimator of Conditional Median

This paper deals with the estimation in nonparametrio regression model.Sincethe conditional mean is sensitive to the tail behavior of the conditional distributionof the model,instead conditional median is considered.For estimation of theconditional median,the sequence of the nearest neighbor estimators is shown to beasymptotio normal and consistent.

ASYMPTOTIC BEHAVIOR OF UNSTABLE ARMA PROCESSES WITH APPLICATION TO LEAST SQUARES ESTIMATES OF THEIR PARAMETERS

A time series x(t), t≥1, is said to be an unstable ARMA process if x(t) satisfies an unstableARMA model such asx(t)=a_1x(t-1)+a_2x(t-2)+…+a_8x(t-s)+w(t)where w(t) is a stationary ARMA process; and the characteristic polynomial A(z)=1-a_1z-a_2z^2-…-a_3z^3 has all roots on the unit circle. Asymptotic behavior of sum form 1 to n (x^2(t)) will be studied by showing somerates of divergence of sum form 1 to n (x^2(t)). This kind of properties Will be used for getting the rates of convergenceof least squares estimates of parameters a_1, a_2,…, a_?

Asymptotic Estimates to Non-global Solutions of a Multi-coupled Parabolic System

This paper deals with asymptotic behavior of solutions to a parabolic system, where two heat equations with inner absorptions are multi-coupled via inner sources and boundary flux. We determine four kinds of simultaneous blow-up rates under different dominations of nonlinearities in the model. Two characteristic algebraic systems associated with the problem are introduced to get very simple descriptions for the four simultaneous blow-up rates as well as the known critical exponents, respectively. It is observed that the blow-up rates are independent of the nonlinear inner absorptions.

Efficient Estimation of a Varying-coefficient Partially Linear Binary Regression Model

This article considers a semiparametric varying-coefficient partially linear binary regression model. The semiparametric varying-coefficient partially linear regression binary model which is a generalization of binary regression model and varying-coefficient regression model that allows one to explore the possibly nonlinear effect of a certain covariate on the response variable. A Sieve maximum likelihood estimation method is proposed and the asymptotic properties of the proposed estimators are discussed. One of our main objects is to estimate nonparametric component and the unknowen parameters simultaneously. It is easier to compute, and the required computation burden is much less than that of the existing two-stage estimation method. Under some mild conditions, the estimators are shown to be strongly consistent. The convergence rate of the estimator for the unknown smooth function is obtained, and the estimator for the unknown parameter is shown to be asymptotically efficient and normally distributed. Simulation studies are carried out to investigate the performance of the proposed method.

Efficient Estimation for Semiparametric Varying-Coefficient Partially Linear Regression Models with Current Status Data

This article considers a semiparametric varying-coefficient partially linear regression model with current status data. The semiparametric varying-coefficient partially linear regression model which is a generalization of the partially linear regression model and varying-coefficient regression model that allows one to explore the possibly nonlinear effect of a certain covariate on the response variable. A Sieve maximum likelihood estimation method is proposed and the asymptotic properties of the proposed estimators are discussed. Under some mild conditions, the estimators are shown to be strongly consistent. The convergence rate of the estimator for the unknown smooth function is obtained and the estimator for the unknown parameter is shown to be asymptotically efficient and normally distributed. Simulation studies are conducted to examine the small-sample properties of the proposed estimates and a real dataset is used to illustrate our approach.

Asymptotic estimates for slowly rotating Newtonian stars

This work is mainly concerned with the rotating Newtonian stars with prescribed angular velocity law existence of rotating star solutions For general compressible fluids, the was proved by using concentration- compactness principle. In this paper, we establish the asymptotic estimates on the diameters of the stars with small rotation. The novelty of this paper is that a direct and concise definition of slowly rotating stars is given, different from the case with given angular momentum law, and the most general fluids are considered.

Asymptotic estimate of a twisted Cauchy-Riemann operator with Neumann boundary condition

Abstract For a holomorphic function f defined on a strongly pseudo-convex domain in Cn such that it has only isolated critical points, we define a twisted Cauchy-Riemann operator -δτf ：-δ＋τδf∧. We will give an asymptotic estimate of the corresponding harmonic forms as T tends to infinity. This asymptotic estimate is used to recover the residue pairing of the singularity defined by f.

Global Attractors for a Nonclassical Diffusion Equation

We prove the existence of global attractors in H0^1 （Ω） for a nonclassical diffusion equation. Two types of nonlinearity f are considered： one is the critical exponent, and the other is the polynomial growth of arbitrary order.

Ruin Probabilities for a Two-Dimensional Perturbed Risk Model with Stochastic Premiums

In this paper, we consider a two-dimensional perturbed risk model with stochastic premiums and certain dependence between the two marginal surplus processes. We obtain the Lundberg-type upper bound for the infinite-time ruin probability by martingale approach, discuss how the dependence affects the obtained upper bound and give some numerical examples to illustrate our results. For the heavy-tailed claims case, we derive an explicit asymptotic estimation for the finite-time ruin probability.

The Ruin Probability of the Renewal Model with Constant Interest Force and Upper-tailed Independent Heavy-tailed Claims

In this paper, we obtain the uniform estimate for discounted aggregate claims in the continuous-time renewal model of upper-tailed independent and heavy-tailed random variables. With constant interest force and constant premium rate, we establish a uniform simple asymptotic formula for ruin probability of the renewal model in the case where the initial surplus is large.