可允许集上的广义向量拟均衡问题

主要讨论可允许集上的广义向量拟均衡问题,推广L in的一些结果.     

A NOTE ON SAMPLE PATH PROPERTIES OF l~p-VALUED GAUSSIAN PROCESSES

§ 1　Introduction and ResultsLet{Y(t) ,t≥ 0 }={Xk(t) ,t≥ 0 }∞k=1 be a sequence of independent Gaussian processeswith EXk(t) =0 and stationary incrementsσ2k(h) =E(Xk(t h) -Xk(t) ) 2 ,where through-outthis paper,σ2k(h) is assumed to be a non-decreasing continuous function foreach k≥ 1 .For p≥ 1 ,putσ(p,h) = ∞k=1σpk(h) 1 /p, (1 .1 )σ* (h) =maxk≥ 1 σk(h) , (1 .2 )σ～ (p,h) =σ(2 p/(2 -p) ,h) ,if 1≤ p <2 ,σ* (h) ,if p≥ 2 ,(1 .3)δpp =E|N(0 ,1 ) |p =2 p/2π∫∞0 x(p- 1 ) /2 e- …     

关于l^P值Gauss过程的快点

该文证明了l^p值Gauss过程发生无限次例外振动的点集是一随机分形，并且给出了点击概率的一个临界值.     

Asymptotic inference for stochastic processes

This is a survey of some aspects of large-sample inference for stochastic processes. A unified framework is used to study the asymptotic properties of tests and estimators parameters in discrete-time, continuous-time jump-type, and diffusion processes. Two broad families of processes, viz, ergodic and non-ergodic type are introduced and the qualitative differences in the asymptotic results for the two families are discussed and illustrated with several examples. Some results on estimation and testing via Bayesian, nonparametric, and sequential methods are also surveyed briefly.     

一类集值投入产出方程的可解性结果

A class of set-valued Leontief input-output equation is introduced and two solvability theorems are obtmned,which provide some corresponding existence,surjection as well as continuity results.     

Relaxation and existence of optimal controls for systems governed by evolution inclusions in separable Banach spaces

In this paper, we examine relaxed control systems governed by evolution inclusions in a separable Banach space. First, we establish the existence of admissible trajectories, correcting an earlier result of Ahmed. Then, we obtain a compactness result for the set of admissible trajectories. Using this compactness result, we prove the existence of optimal solutions for optimal control problems; furthermore, we show that the values of the original and relaxed problems are equal. Finally, we show that the original trajectories are dense in the set of relaxed trajectories. An example is worked out.This research was supported by NSF Grant No. DMS-86-02313.     

广义凸空间上重合点定理和极大极小不等式

利用已知的KKM型定理,在广义空间上得到若干个新的重合点定理和推广的Fan-Browder型不动点定理,并且讨论了Von Newmann-Sion型极大极小不等式.主要结果改进和推广了文献中的相应结论.     

随机过程增量不等式的推广

本文将推广在［３］中由Ｅ．Ｃｓａｋｉ及Ｍ．Ｃｓｏｒｇｏ所引入的关于随机过程不等式，并把它应用到某些随机过程中，从而得到这些随机过程的一些极限定理．     

含估计参数的加权经验过程

在讨论(广义)非参数似然比拟合优度检验时,加权经验过程理论是一个非常重要的基础.但对含估计参数的加权经验过程理论,目前文献中很少讨论.对含估计参数的加权经验过程的上界型和积分型两种统计量的近似分布进行了讨论,给出了较一般的结果.所得结论叮以为进一步讨论复合零假设下(广义)非参似然比拟合优度检验提供理论基础.     

Moment Solutions for the State Exiting Counting Processes of a Markov Renewal Process

Important performance measures for many Markov renewal processes are the counts of the exits from each state. We present solutions for the conditional first, second, and covariance moments of the state exiting counting processes for a Markov renewal process, and solutions for the unconditional equilibrium versions of the moments. We demonstrate the relationship between the conditional first moments for the state exiting and the state entering counting processes. For analytical and illustrative purposes, we concentrate on the two state case. Two asymptotic expansions for the moment functions are proposed and evaluated both analytically and empirically. The two approximations are shown to be competitive in terms of absolute relative error, but the second approximation has a simpler analytical form which is useful in analyzing more complex stochastic processes having an underlying MRP structure.     

Approximations to permutation and exchangeable processes

We obtain weighted approximations by a Brownian bridge to permutation and exchangeable processes and to appropriately defined inverse processes. Our results provide as special cases useful weighted approximations to the uniform empirical and quantile processes and to generalized bootstrapped versions of these processes. A number of other applications are discussed. Our approach is based on the Skorokhod embedding for martingales.     

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本文中我们给出了生灭过程的轨道结构,指出轨道结构与构造理论之间的一一对应关系,并且利用Ito游程理论说明构造理论中各个参数的概率含义.     

Connection between deriving bridges and radial parts from multidimensional Ornstein-Uhlenbeck processes

Summary First we give a construction of bridges derived from a general Markov process using only its transition densities. We give sufficient conditions for their existence and uniqueness (in law). Then we prove that the law of the radial part of the bridge with endpoints zero derived from a special multidimensional Ornstein--Uhlenbeck process equals the law of the bridge with endpoints zero derived from the radial part of the same Ornstein--Uhlenbeck process. We also construct bridges derived from general multidimensional Ornstein--Uhlenbeck processes.     

Entropy Maximization for Markov and Semi-Markov Processes

The literature about maximum of entropy for Markov processes deals mainly with discrete-time Markov chains. Very few papers dealing with continuous-time jump Markov processes exist and none dealing with semi-Markov processes. It is the aim of this paper to contribute to fill this lack. We recall the basics concerning entropy for Markov and semi-Markov processes and we study several problems to give an overview of the possible directions of use of maximum entropy in connection with these processes. Numeric illustrations are presented, in particular in application to reliability.     

Estimates for distances between first exit times via parabolic equations in unbounded cylinders

First exit times and their dependence on variations of parameters are studied for diffusion processes with non-stationary coefficients. Estimates of L_p-distances and some other distances between two exit times are obtained. These estimates are based on some new prior estimates for solutions of parabolic Kolmogorovs equations with infinite horizon without Cauchy conditions.Mathematics Subject Classifications (2000): 60G17, 60G40, 60J50, 60J60, 60J65     

Some time change representations of stable integrals, via predictable transformations of local martingales

From the predictable reduction of a marked point process to Poisson, we derive a similar reduction theorem for purely discontinuous martingales to processes with independent increments. Both results are then used to examine the existence of stochastic integrals with respect to stable Lévy processes, and to prove a variety of time change representations for such integrals. The Knight phenomenon, where possibly dependent but orthogonal processes become independent after individual time changes, emerges as a general principle.     

A characterization of mixing processes of type G1

A stationary Gaussian process is mixing if and only if its covariance function tends to zero as the lag increases to infinity. We give an analogous characterization for a large class of symmetric infinitely divisible processes, known as processes of type G, whose marginal distribution are variance mixtures of the normal distribution.The first author is also associated with the Hugo Steinhaus Center for Stochastic Methods, Poland. The second author was partially supported by the ONR Grant N00014-90-J-1287 at Boston University and by a grant of the United States-Israel Binational Science Foundation.     

Generalized Inv-Log-Gamma-G processes

Abstract

Gamma processes belong to subordinators for which very small jumps occurs infinitely many times in any finite time interval but their sums are finite. Here we consider their novel and important modifications with a nice application potential. A generalization of fractional kth lower record value process defined in Bieniek and Szynal, called Inverse-Log-Gamma-G process is investigated. Explicit relation with the Gamma process is presented and conditional, posterior and finite dimensional distributions are derived. The results are obtained by appropriate transformations of known stochastic processes. In contrast with the regression this allows us to describe the finite dimensional distributions of the processes of interest and in this way to make their full characterization.     

两参数齐次独立增量过程在原点的局部性质

Ａｄｌｅｒ曾经给出了两参数独立增量过程的特征函数的一般形式．本文对齐次情形给出了更具体的表达式，引进了累积量的概念．在此基础上，研究了比值Ｘ（ｓ，ｔ）／ｓｔ在原点的分布，单调过程在原点的局部性质以及任意过程在原点的局部增长．由此得到了Ｂｒｏｗｎ单和不包含高斯分量的过程在原点的局部增长．     

Poisson’s equation for discrete-time single-birth processes

We consider Poisson’s equation for discrete-time single-birth processes, and we derive its solutions by solving a linear system of infinitely many equations. We apply the solution of Poisson’s equation to obtain the asymptotic variance. The results are further applied to birth–death processes and the scalar-valued GI/M/1-type Markov chains.