This paper concerns the square-mean almost automorphic solutions to a class of abstract semilin- ear functional integro-differential stochastic evolution equations in real separable Hilbert spaces. Under some suitable assumptions, the existence, uniqueness and asymptotic stability of the square-mean almost automorphic mild solution to some stochastic differential equations are established. As an application, we analyze the almost automorphic mild solution to some stochastic partial functional differential equation which turns out to be in good agreement with our abstract results.
In this paper, we study the GJR scaling model which embeds the intraday return processes into the daily GJR model and propose a class of robust M-estimates for it. The estimation procedures would be more efficient when high-frequency data is taken into the model. However, high-frequency data brings noises and outliers which may lead to big bias of the estimators. Therefore, robust estimates should be taken into consideration. Asymptotic results are derived from the robust M-estimates without the finite fourth moment of the innovations. A simulation study is carried out to assess the performance of the model and its estimates. Robust M-estimate of GJR model is also applied in predicting VaR for real financial time series.
In this article, we prove the local wellposedness of Three-Dimensional incompressible magneto- hydrodynamic system (MHD) with initial data in the critical spaces, without assumptions of small density variation.
In this paper we investigate the robust estimation of generalized varying coefficient models in which the unknown regression coefficients may change with different explanatory variables. Based on the B-spline series approximation and Walsh-average technique we develop an initial estimator for the unknown regression coefficient functions. By virtue of the initial estimator, the generalized varying coefficient model is reduced to a univariate nonparametric regression model. Then combining the local linear smooth and Walsh average technique we further propose a two-stage local linear Walsh-average estimator for the unknown regression coefficient functions. Under mild assumptions, we establish the large sample theory of the proposed estimators by utilizing the results of U-statistics and shows that the two-stage local linear Walsh-average estimator own an oracle property, namely the asymptotic normality of the two-stage local linear Walsh-average estimator of each coefficient function is not affected by other unknown coefficient functions. Extensive simulation studies are conducted to assess the finite sample performance, and a real example is analyzed to illustrate the proposed method.
This paper is concerned with the statistical inference of partially linear varying coefficient dynamic panel data model with incidental parameter, including efficient estimation of the parametric and nonparametric components and consistent determination of the lagged order. For the parametric component, we propose an efficient semiparametric generalized method-of-moments (GMM) estimator and establish its asymptotic nor- mality. For the nonparametric component, B-spline series approximation is employed to estimate the unknown coefficient functions, which are shown to achieve the optimal nonparametric convergence rate. A consistent estimator of the variance of error component is also constructed. In addition, by using the smooth-threshold GMM estimating equations, we propose a variable selection method to identify the significant order of lagged terms automatically and remove the irrelevant regressors by setting their coefficient to zeros. As a result, it can consistently determine the true lagged order and specify the significant exogenous variables. Further studies show that the resulting estimator has the same asymptotic properties as if the true lagged order and signifi- cant regressors were known prior, i.e., achieving the oracle property. Numerical experiments are conducted to evaluate the finite sample performance of our procedures. An example of application is also illustrated.
We are concerned with a time-dependent Ginzburg-Landau equations come from the superfluid atomic Fermi-gases near the Feshbach resonance from the fermion-boson model. We obtain the global existence and uniqueness of solutions to the TDGL equations near the BCS-BEC crossover.
In this paper, we consider a general composite convex optimization problem with a cone-convex system in locally convex Hausdorff topological vector spaces. Some Fenchel conjugate transforms for the com- posite convex functions are derived to obtain the equivalent condition of the Stable Farkas Lemma, which is formulated by using the epigraph of the conjugates for the convex functions involved and turns out to be weaker than the classic Slater condition. Moreover, we get some necessary and sufficient conditions for stable duality results of the composite convex functions and present an example to illustrate that the monotonic increasing property of the outer convex function in the objective function is essential. Our main results in this paper develop some recently results.
The present paper deals with results of stability/instability of solitary waves with nonzero asymp- totic value for a microstructure PDE. By the exact solitary wave solutions and detailed computations, we set up the explicit expression for the discrimination d"(c). Finally, a complete study of orbital stablity/instablity for the explicit exact solutions is given.
The nonlocal nonlinear boundary value problem with turning point is considered. Leading the stretched variables the formal asymptotic solution of the original problem is constructed. And by using the theory of differential inequalities the existence and uniformly validity of solution for the original boundary value problems are proved. The contribution of this paper is that, the asymptotic behavior of solution is studied by using a simple and special method.
In this paper we are concerned with the regularity of solutions to the Navier-Stokes equations with the condition on the pressure on parts of the boundary where there is flow. For the steady Stokes problem a result similar to Lq-theory for the one with Dirichlet boundary condition is obtained. Using the result, for the steady Navier-Stokes equations we obtain regularity as the case of Dirichlet boundary conditions. Furthermore, for the time-dependent 2-D Navier-Stokes equations we prove uniqueness and existence of regular solutions, which is similar to J.M.Bernard's results[6] for the time-dependent 2-D Stokes equations.
In this paper, we apply the symmetric Galerkin methods to the numerical solutions of a kind of singular linear two-point boundary value problems. We estimate the error in the maximum norm. For the sake of obtaining full superconvergence uniformly at all nodal points, we introduce local mesh refinements. Then we extend these results to a class of nonlinear problems. Finally, we present some numerical results which confirm our theoretical conclusions.
In this paper, the higher order NLS equation with cubic-quintic nonlinear terms is studied, new abundant solitary solutions with traveling-wave envelope of this equation are obtained with the aid of a gener- alized auxiliary equation method and complex envelope non-traveling transform approach.
We consider the existence, both locally and globally in time, as well as the asymptotic behavior of solutions for the Cauchy problem of the sixth-order Boussinesq equation with damping term. Under rather mild conditions on the nonlinear term and initial data, we prove that the above-mentioned problem admits a unique local solution, which can be continued to a global solution, and the problem is globally well-posed. Finally, under certain conditions, we prove that the global solution decays exponentially to zero in the infinite time limit.
The celebrated H-theorem of Boltzmann has important physical significance. The H-theorem states that entropy cannot diminish, and that the distribution function f(z, t) must tend towards its equilibrium state. In this paper, using the relationship between solutions of Boltzmann equation and the two-particle Boltzmann equation system, we obtain three forms of Two-Particle Boltzmann H-theorem from the two-particle Boltzmann equation system of BBGGKY hierarchy, and give an application example for the Two-Particle Boltzmann H- theorem. Also, the relation between entropy and the Two-Particle Boltzmann H-theorem is obtained.
The aim of the present communication is to discuss the analytical solution for the unsteady flow of a third grade fluid which occupies the space y > 0 over an infinite porous plate. The flow is generated due to the motion of the plate in its own plane with an impulsive velocity V (t). Translational symmetries in variables t and y are utilized to reduce the governing non-linear partial differential equation into an ordinary differential equation. The reduced problem is then solved using homotopy analysis method (HAM). Graphs representing the solution are plotted and discussed and proper conclusions are drawn.
Travelling wave solutions of integro-differential equations for modeling one-dimensional neuronal networks, are studied. Under moderate continuity assumptions, necessary and sufficient conditions for the existence and uniqueness of monotone increasing (decreasing) Travelling wave solutions are established. Some faults in previous studies are corrected.
In this paper, the positive steady states of the epidemic model with non-monotonic incidence rate are considered. Firstly, it is proved that the unique positive constant steady state is stable for the ODE system and the PDE system. Secondly, a priori estimate of positive steady states is given, and the non-existence of non-constant positive steady states is established by using Poincare inequality and Young inequality. Finally, the existence and bifurcation of non-constant positive steady states are studied by using the degree theory and the global bifurcation theorem.
The exponential stabilization problem of a robot-camera system with unknown camera parameters is investigated. Based on the visual feedback and the state-input transformation, an uncertain chained form model is presented for a type of nonholonomic mobile robots. Then, a new time-varying feedback controller is proposed to stabilize the uncertain system exponentially with the help of the stabilization theorems, state-scaling and switching techniques. The exponential stability of the closed-loop system is rigorously proved. Simulation results are given to demonstrate the effectiveness of the proposed strategies.
Two Latin squares of order v are r-orthogonal if their superposition produces exactly r distinct ordered pairs. The two squares are said to be r-orthogonal idempotent Latin squares and denoted by r-MOILS(v) if they are all idempotent. In this paper, we show that for any integer v ≧ 28, there exists an r-MOILS(v) if and only if r∈[v, v2]\{v + 1, v2-1}.
In this paper, we consider the empirical likelihood-based inferences for varying coefficient models Y = Xτα(U) + ε when X are subject to missing at random. Based on the inverse probability-weighted idea, a class of empirical log-likelihood ratios, as well as two maximum empirical likelihood estimators, are developed for α(U). The resulting statistics are shown to have standard chi-squared or normal distributions asymptotically. Simulation studies are also constructed to illustrate the finite sample properties of the proposed statistics.
Generalized case-cohort design has been proved to be a cost-effective way to enhance the efficiency of large epidemiological cohort. In this article, we propose an inference procedure for estimating the unknown parameters in Cox's proportional hazards model in generalized case-cohort design and establish an optimal sample size allocation to achieve the maximum power at a given budget. The finite sample performance of the proposed method is evaluated through simulation studies. The proposed method is applied to a real data set from the National Wilm's Tumor Study Group.
