共查询到20条相似文献,搜索用时 640 毫秒
1.
Shin Ichi Aihara 《Acta Appl Math》1994,35(1-2):131-151
The purpose of this paper is to study the identification problem of a spatially varying discontinuous parameter in stochastic hyperbolic equations. In previous works, the consistency property of the maximum likelihood estimate (MLE) was explored and the generating algorithm for MLE proposed under the condition that an unknown parameter is in a sufficiently regular space with respect to spatial variables.In order to show the consistency property of the MLE for a discontinuous coefficient, we use the method of sieves, i.e. the admissible class of unknown parameters is projected into a finite-dimensional space. For hyperbolic systems, we cannot obtain a regularity property of the solution with respect to a parameter. So in this paper, the parabolic regularization technique is used. The convergence of the derived finite-dimensional MLE to the infinite-dimensional MLE is justified under some conditions. 相似文献
2.
A non-Archimedean Banach space has the orthogonal finite-dimensional decomposition property(OFDDP) if it is the orthogonal direct sum of a sequence of finite-dimensional subspaces.This property has an influence in the non-Archimedean Grothendieck's approximation theory,where an open problem is the following: Let E be a non-Archimedean Banach space of countable type with the OFDDP and let D be a closed subspace of E.Does D have the OFDDP? In this paper we give a negative answer to this question; we construct a Banach space of countable type with the OFDDP having a one-codimensional subspace without the OFDDP.Next we prove that,however,for certain classes of Banach spaces of countable type,the OFDDP is preserved by taking finite-codimensional subspaces. 相似文献
3.
《Quaestiones Mathematicae》2013,36(2):135-144
Summary Assume that T:L→M is a positive transformation from an arbitrary Riesz space L into a Dedekind complete Riesz space M, and let T=Tc + Ts be the decomposition of T into its integral component Tc and its singular component Ts. In this note we give an elementary proof of the fact that for every o ? u ? L Tc u = inf(snup Tun: o ? un + u), under the conditionns stated above. This generalizes a recent result of C.D. Aliprantis [1]. 相似文献
4.
Pietro Aiena 《Journal of Mathematical Analysis and Applications》2008,342(2):830-837
This note is a continuation of a previous article [P. Aiena, M.T. Biondi, Property (w) and perturbations, J. Math. Anal. Appl. 336 (2007) 683-692] concerning the stability of property (w), a variant of Weyl's theorem, for a bounded operator T acting on a Banach space, under finite-dimensional perturbations K commuting with T. A counterexample shows that property (w) in general is not preserved under finite-dimensional perturbations commuting with T, also under the assumption that T is a-isoloid. 相似文献
5.
We study the local exponential stabilizability with internally distributed feedback controllers for the incompressible 2D-Navier–Stokes equations with Navier slip boundary conditions. These controllers are localized in a subdomain and take values in a finite-dimensional space. 相似文献
6.
7.
The problem of strong stabilizability of linear systems of neutral type is investigated. We are interested in the case when the system has an infinite sequence of eigenvalues with vanishing real parts. This is the case when the main part of the neutral equation is not assumed to be stable in the classical sense. We discuss the notion of regular strong stabilizability and present an approach to stabilize the system by regular linear controls. The method covers the case of multivariable control and is essentially based on the idea of infinite-dimensional pole assignment proposed in [G.M. Sklyar, A.V. Rezounenko, A theorem on the strong asymptotic stability and determination of stabilizing controls, C. R. Acad. Sci. Paris Ser. I Math. 333 (8) (2001) 807-812]. Our approach is based on the recent results on the Riesz basis of invariant finite-dimensional subspaces and strong stability for neutral type systems presented in [R. Rabah, G.M. Sklyar, A.V. Rezounenko, Stability analysis of neutral type systems in Hilbert space, J. Differential Equations 214 (2) (2005) 391-428]. 相似文献
8.
A. Agrachev S. Kuksin A. Sarychev 《Annales de l'Institut Henri Poincaré (B) Probabilités et Statistiques》2007,43(4):399
The paper is devoted to studying the image of probability measures on a Hilbert space under finite-dimensional analytic maps. We establish sufficient conditions under which the image of a measure has a density with respect to the Lebesgue measure and continuously depends on the map. The results obtained are applied to the 2D Navier-Stokes equations perturbed by various random forces of low dimension. 相似文献
9.
混合误差半参数回归模型估计的相合性 总被引:1,自引:0,他引:1
研究了误差为ψ混合和ψ混合序列的半参数回归模型,综合最小二乘法和非参数权函数估计方法,分别定义了待估参数β和未知函数夕的估计量βm,n和9m,n(χ).利用混合序列的矩不等式及凸函数的性质,在较弱的条件下证明了这些估计量的强相合性与矩相合性,这些结果推广了已有的相应的研究结果. 相似文献
10.
A problem of goodness-of-fit test for ergodic diffusion processes is presented. In the null hypothesis the drift of the diffusion is supposed to be in a parametric form with unknown shift parameter. Two Cramer–von Mises type test statistics are studied. The first test uses the local time estimator of the invariant density, the second one uses the empirical distribution function. The unknown parameter is estimated via the maximum likelihood estimator. It is shown that the limit distribution of the two test statistics does not depend on the unknown parameter, thus both the tests are asymptotically parameter free. Some considerations on the consistency of the proposed tests and some simulation studies are also given. 相似文献
11.
Raimund Bürger Kenneth H. Karlsen Héctor Torres John D. Towers 《Numerische Mathematik》2010,116(4):579-617
Continuously operated clarifier–thickener (CT) units can be modeled by a non-linear, scalar conservation law with a flux that
involves two parameters that depend discontinuously on the space variable. This paper presents two numerical schemes for the
solution of this equation that have formal second-order accuracy in both the time and space variable. One of the schemes is
based on standard total variation diminishing (TVD) methods, and is addressed as a simple TVD (STVD) scheme, while the other
scheme, the so-called flux-TVD (FTVD) scheme, is based on the property that due to the presence of the discontinuous parameters,
the flux of the solution (rather than the solution itself) has the TVD property. The FTVD property is enforced by a new nonlocal
limiter algorithm. We prove that the FTVD scheme converges to a BV
t
solution of the conservation law with discontinuous flux. Numerical examples for both resulting schemes are presented. They
produce comparable numerical errors, while the FTVD scheme is supported by convergence analysis. The accuracy of both schemes
is superior to that of the monotone first-order scheme based on the adaptation of the Engquist–Osher scheme to the discontinuous
flux setting of the CT model (Bürger, Karlsen and Towers in SIAM J Appl Math 65:882–940, 2005). In the CT application there
is interest in modelling sediment compressibility by an additional strongly degenerate diffusion term. Second-order schemes
for this extended equation are obtained by combining either the STVD or the FTVD scheme with a Crank–Nicolson discretization
of the degenerate diffusion term in a Strang-type operator splitting procedure. Numerical examples illustrate the resulting
schemes. 相似文献
12.
We prove that a closed set K of a finite-dimensional space is invariant under the stochastic control system
dX=b(X,v(t))dt+σ(X,v(t))dW(t),v(t)∈U, 相似文献
13.
The article considers unstable infinite-dimensional systems, which may be phase-nonminimal. A derivativefree finite-dimensional adaptive controller is constructed. The controller stabilizes the output process using only the current process value. The method is based on a controller design algorithm for a finite-dimensional phase-nonminimal system with an unmodeled disturbance, which is obtained by finite-dimensional approximation of the initial system. The required prior information is restricted to a domain in the parameter space where the transfer function of the approximating model is irreducible.Translated from Nelineinye Dinamicheskie Sistemy: Kachestvennyi Analiz i Upravlenie — Sbornik Trudov, No. 3, pp. 29–39, 1993. 相似文献
14.
M. V. Balashov 《Mathematical Notes》2002,71(3-4):295-304
15.
We propose an empirical likelihood-based estimation method for conditional estimating equations containing unknown functions, which can be applied for various semiparametric models. The proposed method is based on the methods of conditional empirical likelihood and penalization. Thus, our estimator is called the penalized empirical likelihood (PEL) estimator. For the whole parameter including infinite-dimensional unknown functions, we derive the consistency and a convergence rate of the PEL estimator. Furthermore, for the finite-dimensional parametric component, we show the asymptotic normality and efficiency of the PEL estimator. We illustrate the theory by three examples. Simulation results show reasonable finite sample properties of our estimator. 相似文献
16.
利用增广Lagrange乘子法和自适应法则,得到求解单侧障碍自由边界问题的自适应Uzawa块松弛法.单侧障碍自由边界问题离散为有限维线性互补问题,等价于一个用辅助变量和增广Lagrange函数表示的鞍点问题.采用Uzawa块松弛算法求解该问题得到一个两步迭代法,主要的子问题为一个线性问题,同时能显式求解辅助变量.由于Uzawa块松弛算法的收敛速度显著依赖于罚参数,而且对具体问题很难选择合适的罚参数.为提高算法的性能,提出了自适应法则,该方法自动调整每次迭代所需的罚参数.数值结果验证了该算法的理论分析. 相似文献
17.
孙同军 《高校应用数学学报(英文版)》2001,16(1):63-71
Abastract. In this paper,a streamline-diffusion F. E. M. for linear Sobolev equations with con-vection-dominated term is given. According to the range of space-time F. E mesh parameter h,two choices for artifical diffusion parameter are presented,and for the corresponding computa-tion schemes the stability and error estimates in suitable norms are estabilished. 相似文献
18.
本文研究线性模型中回归参数M估计的强相合性,给出一些较弱的充分条件.与相应结论比较,这里给出的条件对矩的要求有实质性的改进. 相似文献
19.
The consistency proof for the (Gaussian quasi) maximum likelihood estimator in multivariable ARMA models as given in Dunsmuir and Hannan (1976, Adv, in Appl. Probab. 8, 339–364) rests on a certain property of the underlying parameter space, called B6 in their paper. It is not known whether the usual parameter spaces like the manifold M(n) or the parameter spaces corresponding to echelon forms satisfy condition B6, since the argument given by Dunsmuir and Hannan to establish this fact is inconclusive. In Pötscher (1987, J. Multivariate Anal. 21 29–52) it was shown how consistency can be proved without relying on B6 if the data generating process is Gaussian. In this note we show that the Gaussianity assumption can be replaced by ergodicity thus restoring Dunsmuir and Hannan's consistency proof to its full generality and extending it to parameter spaces which do not satisfy condition B6. 相似文献
20.
Birgit Jacob Felix L. Schwenninger Hans Zwart 《Journal of Differential Equations》2019,266(10):6284-6306
We study minimal conditions under which mild solutions of linear evolutionary control systems are continuous for arbitrary bounded input functions. This question naturally appears when working with boundary controlled, linear partial differential equations. Here, we focus on parabolic equations which allow for operator-theoretic methods such as the holomorphic functional calculus. Moreover, we investigate stronger conditions than continuity leading to input-to-state stability with respect to Orlicz spaces. This also implies that the notions of input-to-state stability and integral-input-to-state stability coincide if additionally the uncontrolled equation is dissipative and the input space is finite-dimensional. 相似文献