Limit theorems for bivariate Appell polynomials. Part II: Non-central limit theorems

Summary. Let (X _t ,t∈Z) be a linear sequence with non-Gaussian innovations and a spectral density which varies regularly at low frequencies. This includes situations, known as strong (or long-range) dependence, where the spectral density diverges at the origin. We study quadratic forms of bivariate Appell polynomials of the sequence (X _t ) and provide general conditions for these quadratic forms, adequately normalized, to converge to a non-Gaussian distribution. We consider, in particular, circumstances where strong and weak dependence interact. The limit is expressed in terms of multiple Wiener-It? integrals involving correlated Gaussian measures. Received: 22 August 1996 / In revised form: 30 August 1997     

Liouville–type theorems for semilinear elliptic equations involving the Sobolev exponent

In this article, we prove there are no positive smooth solutions of where satisfies one of the following conditions: (i) K is a subharmonic function in with , and the derivative satisfies where for , for and for . (ii) is nondecreasing along each ray for any unit vector in and . (iii) is nondecreasing in , for and for , where and b are constants. Various generalizations to a more general class of nonlinearities are also considered. Received 7 May 1996; in final form 6 January 1997     

Central limit theorems for arrays of decimated linear processes

Linear processes are defined as a discrete-time convolution between a kernel and an infinite sequence of i.i.d. random variables. We modify this convolution by introducing decimation, that is, by stretching time accordingly. We then establish central limit theorems for arrays of squares of such decimated processes. These theorems are used to obtain the asymptotic behavior of estimators of the spectral density at specific frequencies. Another application, treated elsewhere, concerns the estimation of the long-memory parameter in time series, using wavelets.     

关于直接调节系统的绝对稳定性

<正> 非线性自动调节系统的绝对稳定性问题最初是由讨论飞机自动驾驶仪引起的.它的一般化是讨论带有一个非线性执行机构的系统     

常微分方程的區域分析理論(Ⅲ)

<正> 本文是繼續[Ⅰ],[Ⅱ]的發展,並初步總結其中若干部分,定名為分區線性方程.總結其特性及簡易的定性處理法,使這類的非線性方程的規律性非常容易掌握;正如我們掌握常係數線性方程一樣.     

Distribution of Eigenvalues of Real Symmetric Palindromic Toeplitz Matrices and Circulant Matrices

Consider the ensemble of real symmetric Toeplitz matrices, each independent entry an i.i.d. random variable chosen from a fixed probability distribution p of mean 0, variance 1, and finite higher moments. Previous investigations showed that the limiting spectral measure (the density of normalized eigenvalues) converges weakly and almost surely, independent of p, to a distribution which is almost the standard Gaussian. The deviations from Gaussian behavior can be interpreted as arising from obstructions to solutions of Diophantine equations. We show that these obstructions vanish if instead one considers real symmetric palindromic Toeplitz matrices, matrices where the first row is a palindrome. A similar result was previously proved for a related circulant ensemble through an analysis of the explicit formulas for eigenvalues. By Cauchy’s interlacing property and the rank inequality, this ensemble has the same limiting spectral distribution as the palindromic Toeplitz matrices; a consequence of combining the two approaches is a version of the almost sure Central Limit Theorem. Thus our analysis of these Diophantine equations provides an alternate technique for proving limiting spectral measures for certain ensembles of circulant matrices. A. Massey’s current address: Department of Mathematics, UCLA, Los Angeles, CA 90095, USA. e-mail: amassey3102@math.ucla.edu.     

Sturm type theorems for general quasi-variational nonlinear problems

Consider the general equation associated to the initial-value problem where is a restoring force and Q represents a nonlinear damping term. Through an analysis of the equation, we give precise estimates of b in terms of the initial data that extend some results derived from Sturm comparison theorems for linear differential equations of second order. In particular, we show some important theorems of non existence of radial solutions of Dirichlet problems in that either significantly improve the former ones, with the m-Laplacian operator, or cover cases never appeared before, with the mean curvature operator. Received July 18, 1996     

Some central limit theorems for ℓ∞-valued semimartingales and their applications

Summary. This paper is devoted to the generalization of central limit theorems for empirical processes to several types of ℓ^∞(Ψ)-valued continuous-time stochastic processes t⇝X _t ⁿ =(X _t ^{n ,ψ}|ψ∈Ψ), where Ψ is a non-empty set. We deal with three kinds of situations as follows. Each coordinate process t⇝X _t ^{n ,ψ} is: (i) a general semimartingale; (ii) a stochastic integral of a predictable function with respect to an integer-valued random measure; (iii) a continuous local martingale. Some applications to statistical inference problems are also presented. We prove the functional asymptotic normality of generalized Nelson-Aalen's estimator in the multiplicative intensity model for marked point processes. Its asymptotic efficiency in the sense of convolution theorem is also shown. The asymptotic behavior of log-likelihood ratio random fields of certain continuous semimartingales is derived. Received: 6 May 1996 / In revised form: 4 February 1997     

Competitive newsvendor problems with the same Nash and Stackelberg solutions

Consider two newsvendors: (i) they compete satisfying substitutable demands searching Nash equilibrium or (ii) one is the leader deciding first, the other responds optimally playing a Stackelberg game. The leader profits more than she does in (i). We present conditions under which the leader's profit does not improve from (i) to (ii).     

Polyhedral extensions of some theorems of linear programming

Three theorems of linear programming form our starting point: Tucker's theorem (1956) concerning the existence of optimal solutions satisfying the complementary slackness conditions strictly, and Williams' two theorems (1970) concerning the coordinatewise complementary behavior of feasible and optimal solutions. Here, we establish that the same phenomena hold in another, more versatile framework involving general polyhedral convexity. As one main application, the results are transferred into the context of the monotone complementarity problem. Several other theoretical applications are indicated.Research supported in part by the National Science Foundation under grant number MCS 79-05793 at the University of Illinois at Urbana-Champaign.     

On the smallest maximal increment of partial sums of i.i.d. random variables

Summary. We study the almost sure limiting behavior of the smallest maximal increment of partial sums of independent identically distributed random variables for a variety of increment sizes , where is a sequence of integers satisfying , and going to infinity at various rates. Our aim is to obtain universal results on such behavior under little or no assumptions on the underlying distribution function. Received: 30 August 1995 / In revised form: 27 September 1996     

一类二阶多点时标边值问题无界解的存在性

借助不动点定理研究边值问题(φp(u△(t)))▽+f(t,u(t))=0,t∈(0,∞)Tu(0)=∑m-2i=1αiu(ηi),φp(u△(∞))=∑m-2i=1βiφp(u△(ηi))多个正解的存在性,得到了正解存在的充分条件.     

Limit theorems for random symmetric functions

In this paper, based on theorems for limit distributions of empirical power processes for the i.i.d. case and for the case with independent triangular arrays of random variables, we prove limit theorems for U- and V-statistics determined by generalized polynomial kernel functions. We also show that under some natural conditions the limit distributions can be represented as functionals on the limit process of the normed empirical power process. We consider the one-sample case, as well as multi-sample cases. Dedicated to Professor V. M. Zolotarev on his sixty-fifth birthday. Supported by the Hungarian National Foundation for Scientific Research (grant No. T1666). Proceedings of the Seminar on Stability Problems for Stochastic Models, Moscow, Russia, 1996, Part I.     

Neutral delay differential equations with positive and negative coefficients

Consider the neutral delay differential equation [display math001] where [display math002] We studied the asymptotic behavior of the nonoscillatory solutions of Eq. (1) and we obtained sufficient conditions for the oscillation of all solutions, all bounded solutions, and all unbounded solutions of Eq. (1)     

Krull-Schmidt theorems in dimension 1

Let be a semiprime, module-finite algebra over a commutative noetherian ring of Krull dimension 1. We find necessary and sufficient conditions for the Krull-Schmidt theorem to hold for all finitely generated -modules, and necessary and sufficient conditions for the Krull-Schmidt theorem to hold for all finitely generated torsionfree -modules (called ``-lattices' in integral representation theory, and ``maximal Cohen-Macaulay modules' in the dimension-one situation in commutative algebra).

     

ASYMPTOTICS AND OSCILLATION FOR FIRST ORDER MIXED NEUTRAL DIFFERENTIAL EQUATIONS

1IntroductionConsidertheneutraldifferentialequationswherepiERfori=l,2,...,m;o相似文献   

Linearized oscillation theorems for neutral difference equations

Consider the nonlinear neutral difference equation {fx149-1} We establish a linearized oscillation theorem which is a discrete result of the open problem by Gyori and Ladas. This work is partially supported by NNSF (NO: 19671027) of China.     

一种改进的半参数极大似然法估计量的渐近性质

本文研究线性回归模型, Y=β'X+∈,并假设Y可被右删失,∈的分布函 数F0未知.本文证明,在某些条件下, β的一种改进的半参数极大似然法估计量β 有相合性. 同时证明,如果F0不连续,则P{β≠βi.o.}=0.这意味着以概率为一, 当样本很大时, β=β.文献中的现有估计量未见有关于这一性质的报道.相反,包括 Buckley-James估计量及M-估计量在内的大多数的估计量,都不满足这一性质.     

Almost sure limit theorems for stable distributions

Consider a sequence of i.i.d. random variables in the domain of attraction of a stable distribution with an exponent in (0,2]. A universal result in almost sure limit theorem for the partial sums is established. Our results substantially extend and improve those on the almost sure central limit theorem previously obtained by Jonsson 2007, Berkes and Csáki 2001, and Hörmann 2007.     

Interpolation theorems for self-adjoint operators

We prove a complex and a real interpolation theorems on Besov spaces and Triebel-Lizorkin spaces associated with a selfadjoint operator L, without assuming the gradient estimate for its spectral kernel. The result applies to the cases where L is a uniformly elliptic operator or a Schrdinger operator with electro-magnetic potential.