On Time-Reversibility and Estimating Functions for Markov Processes

The time-reversibility of a Markov process implies a particular structure of the score function. It is explored which martingale estimating functions and other unbiased estimating functions have a similar structure. This leads to an estimating function with a semiparametric efficiency property. Also relations to martingale estimating functions based on eigenfunctions of the infinitesimal generator are found.     

关于开区间内连续函数最值的判定

由闭区间上连续函数的最值存在定理,讨论开区间内连续函数最值的存在性,并得出几个结论.     

On the Support of Distributions of Integer-Valued Additive Functions

We obtain a characterization of a set of additive functions with asymptotically finite support. Additive functions taking integer values on prime powers p ^r are considered.     

Orlicz Sylvester Busemann型函数的极值研究

研究了两个Orlicz Busemann型函数A(K;φ)和I(K;φ;m),建立了A(K_t;φ)和I(K_t;φ;m)的最小值.特别地,在二维平面的情况下,给出了它们的最大值.     

On the Cone of Bounded Lower Semicontinuous Functions

We prove that the cone of bounded lower semicontinuous functions defined on a Tychonoff space X is algebraically and structurally isomorphic and isometric to a convex cone contained in the cone of all bounded lower semicontinuous functions defined on the Stone-Cech compactification βX if and only if the space X is normal. We apply this theorem to the study of relationship between a class of multivalued maps and sublinear operators. Using these results, we obtain new proofs of theorems about continuous selections.__________Translated from Matematicheskie Zametki, vol. 77, no. 6, 2005, pp. 886–902.Original Russian Text Copyright ©2005 by Yu. E. Linke.     

Regularity of Harmonic Functions for Some Markov Chains with Unbounded Range

We consider a class of continuous time Markov chains on ? ^d . These chains are the discrete space analogue of Markov processes with jumps. Under some conditions, as we show, harmonic functions associated with these Markov chains are Hölder continuous.     

On Transience Conditions for Markov Chains and Random Walks

We prove a new transience criterion for Markov chains on an arbitrary state space and give a corollary for real-valued chains. We show by example that in the case of a homogeneous random walk with infinite mean the proposed sufficient conditions are close to those necessary. We give a new proof of the well-known criterion for finiteness of the supremum of a random walk.     

On Rescaled Poisson Processes and the Brownian Bridge

The process obtained by rescaling a homogeneous Poisson process by the maximum likelihood estimate of its intensity is shown to have surprisingly strong self-correcting behavior. Formulas for the conditional intensity and moments of the rescaled Poisson process are derived, and its behavior is demonstrated using simulations. Relationships to the Brownian bridge are explored, and implications for point process residual analysis are discussed.     

非齐次可列马尔可夫过程的轨道性质

§1 状态分类 定义1.1 设I是非负整数集,P={P_(ij)(s,t)|i,j∈I,α≤s≤t≤b}是转移函数矩阵。称P对i在t右标准,若limp_(ii)(t,t+h)=1;称P对i在t左标准,若limP_(ii)(t-h,t)=1.若P对i在t同时为右标准的和左标准的,则称P对i在t标准。若P对i在每个t标准,则称P对i标准。P对i右标准或左标准与此类似。若P对每个i标准,则称P标准。P右标准或左标准与此类似(参看[5]、[6])。     

On the Conservativeness of Some Markov Processes

We give a unified method to obtain the conservativeness of a class of Markov processes associated with lower bounded semi-Dirichlet forms on L ²(X;m), including symmetric diffusion processes, some non-symmetric diffusion processes and jump type Markov processes on X, where X is a locally compact separable metric space and m is a positive Radon measure on X with full topological support. Using the method, we give an example in each section, providing the conservativeness of the processes, that are given by the “increasingness of the volume of some sets(balls)” and “that of the coefficients on the sets” of the Markov processes.     

On the Generation of Markov Decision Processes

Comparisons of the performance of solution algorithms for Markov decision processes rely heavily on problem generators to provide sizeable sets of test problems. Existing generation techniques allow little control over the properties of the test problems and often result in problems which are not typical of real-world examples. This paper identifies the properties of Markov decision processes which affect the performance of solution algorithms, and also describes a new problem generation technique which allows all of these properties to be controlled.     

样本函数条件极值中减低偏差的方法

对样本函数条件极值中偏差项的阶进行了分析,探讨了减低偏差项的方法,分析表明古典折刀法、减-d折刀法均不能减低偏差项;在此基础上,提出了减低偏差项的自助法,并论证了在均方误差意义下,θnab是一种较优的估计.     

On Fixed Point and Almost Fixed Point Problems of Lower Semicontinuous Type Multivalued Mappings

In the present paper, some new almost fixed point theorems and fixed point theorems for lower semicontinuous type multivalued mappings are obtained in metrizable H-spaces.     

一定条件下样本函数极值的重采样方法

本文对一定条件下样本函数极值的重采样方法进行了研究,给出了γ~2估计的几种方法,包括减-d折刀法、减-1折刀法和自助法；并对得到的统计量的性质进行了分析．     

随机环境中的马氏链状态分类

给出了随机环境中马氏链的特征数和状态的定义,讨论了状态间的传递性,自反性,对称性,是经典马氏链相应结果的一般化.并运用位势方法研究了状态间的关系,它们在极限理论的研究中非常有用.     

On the Nonexplosion and Explosion for Nonhomogeneous Markov Pure Jump Processes

In this paper, we obtain new drift-type conditions for nonexplosion and explosion for nonhomogeneous Markov pure jump processes in Borel state spaces. The conditions are sharp; e.g., the one for nonexplosion is necessary if the state space is in addition locally compact and the Q-function satisfies weak Feller-type and local boundedness conditions. We comment on the relations of our conditions with the existing ones in the literature and demonstrate some possible applications.