一类随机环境下非线性时间序列模型的遍历性分析

本文主要讨论由模型Xn 1=h(en -q(n 1),-en,Xn 1-p(n 1),…Xn) en 1所确定的序列{Xn,n 1}的极限行为.     

右删失数据下的时间序列数据分析

当平稳时间序列{Xn}被另外的平稳序列{Yn}删失后,我们研究{Xn}的协方差,相关系数的估计问题．特别当{Xn}是AR(p)序列时,我们研究AR(p)的参数估计和一步预测问题．给出的估计量是强相合的．计算机模拟结果说明所提供的方法是适用的．     

一类"停走"生成器输出序列符合率的计算

本文考察了"停走"生成器输出序列{Xn}的一个子列{X2n}与原序列{Zn}的符合率问题,并在此基础上推广到更一般的情况,证明了在本文所指的一类钟控模型中,当g(n)=2n时,其输出序列与原序列的符合率达到最大     

一类具有红灯环境下随机游动的极限性态

就某类红灯随机环境下随机游动{Xn}n∈Z ,建立相应的Markov-双链{ηn}n∈Z ={(Xn,Tn)}n∈Z ;并给出在该红灯环境下,{Xn}n∈Z 的发展受红灯环境影响的关系式;以及由此关系式得出:由于红灯环境的影响减缓了{Xn}n∈Z 的发展速度.     

一类马尔可夫序列最大值的极限律

主要研究一类马尔可夫序列{Xn,n≥0}的最大值的极限分布.导出了这类序列最大值和最小值的分布表达式,利用经典极值理论,建立了规范化最大值max{X0,X1,…,Xn}与i.i.d序列{ξn,n≥1}的规范化最大值max{1ξ,2ξ,…,ξn+1}具有相同极限律的条件.     

独立重尾随机变量随机和的大偏差估计

本文研究了一类独立重尾随机变量随机和S（t)∧=∑k=1^N(t)Xk,t≥0的大偏差概率，其中{N(t),t≥0}是一放大晨负整数值随机变量；{Xn,n≥1}是非负，独立随机变量序列，并与{N(t),t≥０}独立。本文的结果将{Xn,n≥１}为独立同分布情形推广到了独立不同分布情形。     

平面上随机级数的性质

研究了平面上系数{Xn,n≥0}为(?)-混合序列在满足,(q>1)等条件下的随机级数的增长性及值分布,得到了比较好的结果．     

离散随机序列加权和的若干极限定理

设{Xn,n≥0}是任意离散随机变量序列,{ank,0≤k≤n,n≥0)是一常数阵列,我们引入随机序列渐近对数似然比的概念,作为表征随机序列的真实概率测度P与参考测度Q之间的差异的度量,用分析方法,得到了随机序列Jamison型加权和的若干随机偏差定理.     

重尾平稳序列的大偏差

本文给出了一类重尾的随机变量序列{Xn,n≥1}的部分和Sn=∑i=1 n Xi与随机和S(t)=∑i=1^N(t) Xi的大偏差结果其中{N(t),t≥)}是一族非负整值的随机变量，{Xn,n≥1}是非负的平稳过程，并且与{N(t),t≥0}独立。本文将独立同分布情形的结果掖到了平稳相依的情形。     

任意N值随机变量序列关于m阶非齐次马氏链的一类小偏差定理

设{Xn,n≥0}为定义在概率空间(Ω,F,P)上在{1,2,…,N}中取值的随机变量序列.设Q为F上的另一概率测度,并且{Xn,n≥0}在Q下为m阶非齐次马氏链.设h(PIQ)为P关于Q相对于{Xn}的样本散度率距离.该文首先研究{Xn,,n≥0}关于m阶非齐次马氏链的m+1元函数平均值的一类小偏差定理.作为推论,得到了{Xn,n≥0}关于m阶非齐次马氏链状态出现频率和熵密度的一类小偏差定理.最后,得到了m阶非齐次马氏链的若干强大数定律和Shannon-McMillan定理.     

Estimates of stability of characterization of additive types of distributions

An estimate of stability of characterization of distribution types is obtained for the case of additive types. Under some conditions, the estimate has the order ε^1/3L(ε), where L(ε) is a slowly varying function. Proceedings of the Seminar on Stability Problems for Stochastic Models, Moscow, Russia, 1996, Part I.     

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...     

一类完全正则半群簇子簇格的性质

本文研究了完全正则半群簇的子簇格［Ｖ＋∩ＰＶ，Ｖ＋∩ＰＶ］的某些格运算性质，我们证明了簇Ｖ＋∩ＰＶ可分解为Ｖ与Ｖ＋∩ＰＶ的并；对任意完全正则半群簇Ｗ，有Ｗ∩（Ｖ∨Ｖ＋∩ＰＶ）＝（Ｗ∩Ｖ）∨（Ｗ∩Ｖ＋∩ＰＶ）．特别地，我们得到了等式Ｖ＋∩ＰＶ＝Ｖ成立的若干条件．     

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.     

Preservation of equivalence of derivations under reduction of depth of formulas

In this paper we consider derivations in the (&, )-fragment of the intuitionistic propositional calculus. As is known, replacement of any occurrence of a formula [F] in a sequent S by an occurrence of the formula [p], where p is a new propositional variable, with the simultaneous addition to the antecedent of the formula F p or p F depending on the sign of the occurrence of F in S, leaves the derivability unchanged. We give a proof of the fact that the natural extension of this transformation to derivations preserves the relation of equivalence of derivations, i.e., transformed derivations are equivalent if and only if the originals are equivalent. (Derivations are considered equivalent if certain of their normal forms coincide, or, what is the same, if their deductive terms coincide.) It is proved that by the iteration of this transformation, each derivation of an arbitrary sequent S can be transformed into a derivation of a sequent S, depending only on S, whose succedent is a variable, and in the antecedent there occur only formulas of the form a,a & b, a b,,(a b) c, a & b c, a (b & c), wherea, b, c are variables. Here if S is balanced, then S is also balanced. (A sequent is called balanced if each variable occurs in it no more than twice.) The familiar correspondence between certain concepts of the theory of categories and concepts of the theory of proofs allows one to assert that there has been constructed a univalent functor, mapping a free Cartesian closed category into itself.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 88, pp. 197–207, 1979.     

Estimate of growth of Lebesgue functions of linear methods of summation

Sufficient conditions are obtained in terms of matrix elements for the boundedness of Lebesgue functions of linear methods of summation of expansions in orthogonal systems of polynomial type.Translated from Matematicheskie Zametki, Vol. 6, No. 3, pp. 277–286, September, 1969.