相依样本下概率密度函数估计的渐近正态

设随机变量 X具有概率密度函数 f (x) ,X1,… ,Xn为 f (x)的样本 ,基于 X1,… ,Xn定义一类 f (x)的估计 fn(x) .本文在 X1,… ,Xn为 α——混合、ρ——混合样本时 ,得到了 fn(x)的渐近正态性     

相依样本下一种近邻密度估计的相合性

设{ Xn}^∞ n=1是R^1中的平稳过程,具有公共的未知密度函数f(x) ,我们研究基于前n个观测值X1,X2,… Xn的f(x)的一种近邻估计fn(x).本文假定{Xn}^∞ n=1O φ-混合或强混合的,在对混合系数φ(n)趋于零的速度的适当限制下,证明了fn(x)的逐点相合性一致强相合性.并得到了这两种相合性强收敛速度.     

NA、PA样本下密度核估计的相合性

设{Xn,n≥1}为同分布的NA或PA随机变量序列，f(x)为X1概率密度函数，基于样本X1，X2，…，Xn，本对密度函数（f(x)的核估计进行了讨论，在适当条件下证明了其强相合和r阶矩相合。     

两密度函数线性小波估计平方差的渐进分布及其应用

设X1…，Xn1和Y1，…，Yn2是分别取自密度fh和f2的i.i.d样本.设fn1和fn2分别是f1和f2基于样本X1，…，Xn1和Y1，…，Yn2的线性小波估计.本文证明了的渐进正态性．作为此结果的应用，构造了假设Ho：f1=f2的拟合优度检验，并且得到了对于“相近”备择下的渐进功效     

球极投影变换核估计及其逐点收敛速度

本文提出了利用一维核函数构造多维密度函数一个新估计的方法.首先利用球极投影变换将具有密度f(x),x∈Rd的样本变换为具有密度g(y),y∈Ωd+1={yy∈Rd+1,‖y‖=1}的样本.其次,建立f与g的关系.最后,利用球面数据密度核估计构造f的一个新估计fn.在核K及密度f(x)满足一定条件(见§1定理1.1)下,获得了(f∧)n到f的逐点强收敛速度.     

指数分布族参数的渐近最优与可容许的经验Bayes估计

在平方损失下 ,构造了指数族 { f(x|λ) =λe-λx,λ >0 ,x >0 }的参数λ的渐近最优与可容许的经验Bayes估计 ,即δn=(n +u + 1n1φ(n) + 1) β1+ βX,其中X1,X2 ,…Xn(历史样本 )和X(当前样本 )独立同分布于 f(x) ,Sn= ni=11n(1+ βXi) ,φ(n) =1n(Sn+ 1n(1+ βX) +v- 1) ,u >0 ,v >0 ,β >0 (已知 )为任意的实数 ,并证明了该估计的收敛速度为O(n- 1)。     

具强迫项高阶非线性中立型差分方程的振动性与渐近性

讨论具强迫项高阶非线性中立型差分方程△m(xn ∑si=1pi(n)xγi(n)) ∑kj=1qj(n)hj(xσj(n))=fn,n=0,1,2,…及其相关联的差分方程△m(xn ∑si=1pi(n)xγi(n)) ∑kj=1qj(n)hj(xσj(n))=0,n=0,1,2,…的振动性与渐近性,得到了所有解振动或趋于零的充分性判据.     

任意随机变量序列泛函的强极限定理(Ⅱ)

当{Xn，n≥0}是任意随机变量序列，fn(x0，…，xn)(n≥1)是R^n 1上有界Borel可测函数时，利用鞅的理论，建立了泛函序列{fn(X0，…，Xn)，n≥1)的强极限定理，作为推论，得出了关于任意随机变量序列到达某些Borel可测集的频率与条件概率之间的关系．     

线性分式函数n次迭代的简便计算

分式线性函数f(x)=(ax b)/(cx d)的n次迭代的计算方法已有很多文章作了讨论,本文介绍一种简便的计算方法,可以很方便地求出fn(x).定理1已知f(x)=(ax b)/(cx d)设f0(x)=x,f1(x)=f(x),fn(x)=f[fn-1(x)](n≥1),a,b,c,d∈R且ad≠bc,c≠0,则fn(x)=(α(qqnn--βppnn))xx ααpβn(-p     

方向数据密度核估计的对数律

设X为取值于k维单位球面上的单位随机向量,具有概率密度函数f(x),X_1,…,X_n为X的n个i.i.d.的观察,讨论f(x)具有形式的核估计,其中K为定义于[0,+∞]上的非负核函数,ω_k为Ω_k上的Lebesque测度,本文建立了fn(x)的对数律,并给出了fn(x)的一致强相合速度。     

Study of the blow-up of solutions of systems of equations of hydrodynamic type

Mathematical Notes - We study the initial boundary-value problem for three-dimensional systems of equations of pseudoparabolic type. The system is similar to the Oskolkov system, but differs from...     

Characterization of types of asymptotic discernibility of families of hypotheses

We give a characterization of the types of asymptotic discernibility of families of hypotheses in the case of hypothetical measures that are not, in general, mutually absolutely continuous. The case when the logarithm of the likelihood ratio admits an asymptotic expansion of the type of an expansion with local asymptotic normality is examined in detail. Examples are studied.Translated fromTeoriya Sluchainykh Protsessov, Vol. 15, pp. 64–71, 1987.     

Distribution of types of symmetry of tensors of high degree

The asymptotic distribution of tensors of degree N in symmetry types is studied in this paper.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 155, pp. 181–186, 1986.     

Singularities of Solutions of One Class of Equations of Continuum Mechanics

We analyze one class of families of integral equations and describe the dependence of the singularities of solutions of integral equations on the dimensions of the families of kernels of equations. On the basis of these results, we propose procedures for the construction of approximate solutions for a small parameter.     

Determination of asymptotic solutions of problems of nonlinear theories of thermoviscoelasticity

It is shown that the asymptotic solution of a problem of the nonlinear theory of thermoviscoelasticity, if it exists, can be found directly from the solution of the asymptotic boundary-value problem without completely solving the starting problem.M. V. Lomonosov Moscow State University. Translated from Mekhanika Polimerov, No. 3, pp. 395–400, May–June, 1976.     

Emptiness of set of points of lower semicontinuity of Lyapunov exponents

We consider parametric families of differential systems with coefficients that are bounded and continuous on the half-line and uniformly in time continuously depend on a real parameter. For each Lyapunov exponent, we construct a family such that the Lyapunov exponent of its systems treated as a function of the parameter is not a lower semicontinuous function for any value of the parameter.