1.

ON MARKOV CHAINS IN SPACETIME RANDOM ENVIRONMENTS





胡迪鹤 胡晓予《数学物理学报(B辑英文版)》,2009年第29卷第1期


In Section 1, the authors establish the models of two kinds of Markov chains in spacetime random environments (MCSTRE and MCSTRE(+)) with abstract state space. In Section 2, the authors construct a MCSTRE and a MCSTRE(+) by an initial distribution Φ and a random Markov kernel (RMK) p(γ). In Section 3, the authors establish several equivalence theorems on MCSTRE and MCSTRE(+). Finally, the authors give two very important examples of MCMSTRE, the random walk in spcetime random environment and the Markov br...

2.

The Invariance Principle for pθ^→ Chain





Di He HU Zheng Yan XIAO《数学学报(英文版)》,2007年第23卷第1期


There are two parts in this paper. In the first part we construct the Markov chain in random environment（MCRE）, the skew product Markov chain and pθ^→ chain from a random transition matrix and a twodimensional probability distribution, and in the second part we prove that the invarianee principle for pθ^→ chain, a more complex nonhomogeneous Markov chain, is true under some reasonable conditions. This result is more powerful.

3.

The existence and uniqueness of qprocess in random environment 被引次数：10





HU DiheSchool of Mathematics and Statistics Wuhan University Wuhan 430072 China 《中国科学A辑(英文版)》,2004年第47卷第5期


We introduce some basic concepts such as random (sub)transition function, qfunction in random environment, gprocess in random environment and some basic lemmas. For any continuous gfunction in random environment, we prove that the gprocess in random environment always exists, and that any gprocess in random environment satisfies the random Kolmogorov backward equation and the minimal gprocess in random environment always exists. When g is a continuous and conservative gfunction in random environment, the necessary and sufficient conditions for the uniqueness of gprocess in random environment are given. Finally the special cases, homogeneous random transition functions and homogeneous gprocesses in random environments are considered.

4.

An L0（F,R）valued Function＇s Intermediate Value Theorem and Its Applications to Random Uniform Convexity





Tie Xin GUO Xiao Lin ZENG《数学学报(英文版)》,2012年第28卷第5期


Let (Ω , F , P ) be a probability space and L0 ( F, R ) the algebra of equivalence classes of real valued random variables on (Ω , F , P ). When L0 ( F, R ) is endowed with the topology of convergence in probability, we prove an intermediate value theorem for a continuous local function from L0 ( F, R ) to L0 ( F, R ). As applications of this theorem, we first give several useful expressions for modulus of random convexity, then we prove that a complete random normed module ( S, · ) is random uniformly convex iff Lp ( S ) is uniformly convex for each fixed positive number p such that 1 p + ∞ .

5.

THE CONSTRUCTION OF MULTITYPE CANONICAL MARKOV BRANCHING CHAINS IN RANDOM ENVIRONMENTS





胡迪鹤《数学物理学报(B辑英文版)》,2006年第26卷第3期


The investigation for branching processes has a long history by their strong physics background, but only a few authors have investigated the branching processes in random environments. First of all, the author introduces the concepts of the multitype canonical Markov branching chain in random environment (CMBCRE) and multitype Markov branching chain in random environment (MBCRE) and proved that CMBCRE must be MBCRE, and any MBCRE must be equivalent to another CMBCRE in distribution. The main results of this article are the construction of CMBCRE and some of its probability properties.

6.

Standard tripoint transition function 被引次数：1





XIE Yuquan School of Mathematics and Computational Science Xiangtan University Xiangtan 411105 China《中国科学A辑(英文版)》,2005年第48卷第7期


It is usually difficult to express a family of tripoint transition function (TTF) by a transition matrix as Markov processes with one parameter. In this paper, we define three kinds of connection matrixes on the states of standard tripoint transition function (STTF) and study their essential character, give a constructive method on the constantvalue standard tripoint transition function and a general expression of the statesymmetric standard tripoint transition function by a sequence of the transition matrixes of special and simple Markov processes with one parameter.

7.

THE ANALYTICAL PROPERTIES FOR HOMOGENEOUS RANDOM TRANSITION FUNCTIONS





胡迪鹤 邱育峰《数学物理学报(B辑英文版)》,2007年第27卷第1期


The concepts of Markov process in random environment and homogeneous random transition functions are introduced. The necessary and sufficient conditions for homogeneous random transition function are given. The main results in this article are the analytical properties, such as continuity, differentiability, random Kolmogorov backward equation and random Kolmogorov forward equation of homogeneous random transition functions.

8.

The Construction of Denumerable qProcesses in Random EnvironmentsThe Existence and Uniqueness





胡迪鹤 胡晓予《数学物理学报(B辑英文版)》,2008年第28卷第2期


The concepts of Markov process in random environment, qmatrix in random environment, and qprocess in random environment are introduced. The minimal qprocess in random environment is constructed and the necessary and sufficient conditions for the uniqueness of qprocess in random environment are given.

9.

THE DECOMPOSITION OF STATE SPACE FOR MARKOV CHAIN IN RANDOM ENVIRONMENT 被引次数：1





胡迪鹤《数学物理学报(B辑英文版)》,2005年第25卷第3期


This paper is a continuation of [8] and [9]. The author obtains the decomposition of state space X of an Markov chain in random environment by making use of the results in [8] and [9], gives three examples, random walk in random environment, renewal process in random environment and queue process in random environment, and obtains the decompositions of the state spaces of these three special examples.

10.

Construction and regularity of transition functions on polish spaces under measurability conditions





Liuer Ye Xianping Guo《应用数学学报(英文版)》,2013年第29卷第1期


This paper concerns the construction and regularity of a transition (probability) function of a nonhomogeneous continuoustime Markov process with given transition rates and a general state space. Motivating from a lot of restriction in applications of a transition function with continuous (in t≥0) and conservative transition rates q(t, x, Λ), we consider the case that q(t,x,Λ) are only required to satisfy a mild measurability (in t≥0) condition, which is a generalization of the continuity condition. Under the measurability condition we construct a transition function with the given transition rates, provide a necessary and sufficient condition for it to be regular, and further obtain some interesting additional results.

11.

GammaDirichlet algebra and applications





Shui Feng Fang Xu《Frontiers of Mathematics in China》,2014年第9卷第4期


The GammaDirichlet algebra corresponds to the decomposition of the gamma process into the independent product of a gamma random variable and a Dirichlet process. This structure allows us to study the properties of the Dirichlet process through the gamma process and vice versa. In this article, we begin with a brief survey of several existing results concerning this structure. New results are then obtained for the large deviations of the jump sizes of the gamma process and the quasiinvariance of the twoparameter PoissonDirichlet distribution. We finish the paper with the derivation of the transition function of the FlemingViot process with parent independent mutation from the transition function of the measurevalued branching diffusion with immigration by exploring the GammaDirichlet algebra embedded in these processes. This last result is motivated by an open R. C. Gritfiths. problem proposed by S. N. Ethier and

12.

Agedependent branching processes in random environments 被引次数：4





YingQiu Li and QuanSheng Liu《中国科学A辑(英文版)》,2008年第51卷第10期


We consider an agedependent branching process in random environments. The environments are represented by a stationary and ergodic sequence ξ = (ξ0,ξ1,...) of random variables. Given an environment ξ, the process is a nonhomogenous GaltonWatson process, whose particles in nth generation have a life length distribution G(ξn) on R , and reproduce independently new particles according to a probability law p(ξn) on N. Let Z(t) be the number of particles alive at time t. We first find a characterization of the conditional probability generating function of Z(t) (given the environment ξ) via a functional equation, and obtain a criterion for almost certain extinction of the process by comparing it with an embedded GaltonWatson process. We then get expressions of the conditional mean EξZ(t) and the global mean EZ(t), and show their exponential growth rates by studying a renewal equation in random environments.

13.

CONSTRUCTION OF REALVALUED MULTIVARIATE WAVELETS





XIAOSHAOLIANG《高校应用数学学报(英文版)》,1995年第10卷第2期


In this paper, we give a method to construct multivariate wavelets for skewsymmetric scaling function. Such wavelets have some desirable properties, e.g., they are realvalued and orthogonal if the scaling function is realvalued and orthonormal respectively.

14.

Successful couplings for a class of stochastic differential equations driven by Lvy processes





LIN HuoNan & WANG Jian《中国科学 数学(英文版)》,2012年第8期


By constructing proper coupling operators for the integrodifferential type Markov generator,we establish the existence of a successful coupling for a class of stochastic differential equations driven by L’evy processes.Our result implies a new Liouville theorem for spacetime bounded harmonic functions with respect to the underlying Markov semigroups,and it is sharp for OrnsteinUhlenbeck processes driven by αstable L’evy processes.

15.

一般Gauss—Markov模型下最小二乘估计是最佳估计的充要条件





林春土《数学研究与评论》,1993年第13卷第3期


In this paper, we discuss the decomposition of the space μ(X : V) and the invariance with respect to the choice of a generalized inverse of matrix X in the general GaussMarkov model. In Theorem 1, we give necessary and sufficient conditions for the least squares estimator P_{xy} = BLUE(Xβ) under the general GaussMarkov model M = {y,Xβ,σ^{2}V}. In Theorem 2, we prove that P_{xy}= BLUE(Xβ) under model M and invariant with respect to the choice of a generalized inverse of matrix X are equivalent.

16.

A random walk with a branching system in random environments 被引次数：1





Yingqiu LI Xu LI Quansheng LIU《中国科学A辑(英文版)》,2007年第50卷第5期


We consider a branching random walk in random environments, where the particles are reproduced as a branching process with a random environment (in time), and move independently as a random walk on Z with a random environment (in locations). We obtain the asymptotic properties on the position of the rightmost particle at time n, revealing a phase transition phenomenon of the system.

17.

Infinitely dimensional control Markov branching chains in random environments 被引次数：5





HU Dihe School of Mathematics and Statistics Wuhan University Wuhan 430072 China《中国科学A辑(英文版)》,2006年第49卷第1期


First of all we introduce the concepts of infinitely dimensional control Markov branching chains in random environments (βMBCRE) and prove the existence of such chains, then we introduce the concepts of conditional generating functionals and random Markov transition functions of such chains and investigate their branching property. Base on these concepts we calculate the moments of the βMBCRE and obtain the main results of this paper such as extinction probabilities, polarization and proliferation rate. Finally we discuss the classification of βMBCRE according to the different standards.

18.

First Passage Models for Denumerable SemiMarkov Decision Processes with Nonnegative Discounted Costs





Yonghui Huang Xianping Guo School of Mathematics Computational Science Sun YatSen University Guangzhou China《应用数学学报(英文版)》,2011年第27卷第2期


This paper considers a first passage model for discounted semiMarkov decision processes with denumerable states and nonnegative costs.The criterion to be optimized is the expected discounted cost incurred during a first passage time to a given target set.We first construct a semiMarkov decision process under a given semiMarkov decision kernel and a policy.Then,we prove that the value function satisfies the optimality equation and there exists an optimal(or eoptimal) stationary policy under suitable conditions by using a minimum nonnegative solution approach.Further we give some properties of optimal policies.In addition,a value iteration algorithm for computing the value function and optimal policies is developed and an example is given.Finally,it is showed that our model is an extension of the first passage models for both discretetime and continuoustime Markov decision processes.

19.

ADDITIVE FUNCTIONALS AND PERTURBATION OF SEMIGROUP





JIN Mengwei YING Jiangang《数学年刊B辑(英文版)》,2001年第22卷第4期


g1. Introduction and PreliminariesSuPpose that X is a right Markov process with state space E and transition sendgrouP(Pt). Given a multiplicative functional M of X, we define for any nonnegative measurablefunction f on E,Qti(x):= p"(f(X)M), x E E, t 2 0.It follows from the multiplicativity of M that (Qt) is also a semigrouP of transition functionson E and usuaJly called a perturbation semigroap of (Pt). The wellknOWn FeynmanKacsendgrouP is a special case where X is a Brownian moti…

20.

CONTACT PROCESS ON HEXAGONAL LATTICE





姚强 李群昌《数学物理学报(B辑英文版)》,2010年第30卷第3期


In this article, we discuss several properties of the basic contact process on hexagonal lattice H, showing that it behaves quite similar to the process on ddimensional lattice Zd in many aspects. Firstly, we construct a coupling between the contact process on hexagonal lattice and the oriented percolation, and prove an equivalent finite spacetime condition for the survival of the process. Secondly, we show the complete convergence theorem and the polynomial growth hold for the contact process on hexagonal lattice. Finally, we prove exponential bounds in the supercritical case and exponential decay rates in the subcritical case of the process.
