The concepts of Markov process in random environment, q-matrix in random environment, and q-process in random environment are introduced. The minimal q-process in random environment is constructed and the necessary an...The concepts of Markov process in random environment, q-matrix in random environment, and q-process in random environment are introduced. The minimal q-process in random environment is constructed and the necessary and sufficient conditions for the uniqueness of q-process in random environment are given.展开更多
This article is a continuation of[9].Based on the discussion of random Kolmogorov forward（backward）equations,for any given q-matrix in random environment, Q（θ）=（q（θ;x,y）,x,y∈X）,an infinite class of q-proces...This article is a continuation of[9].Based on the discussion of random Kolmogorov forward（backward）equations,for any given q-matrix in random environment, Q（θ）=（q（θ;x,y）,x,y∈X）,an infinite class of q-processes in random environments satisfying the random Kolmogorov forward（backward）equation is constructed.Moreover, under some conditions,all the q-processes in random environments satisfying the random Kolmogorov forward（backward）equation are constructed.展开更多
This paper introduces some concepts such as q- process in random environment, Laplace transformation, ergodic potential kernel, error function and some basic lemmas.We study the continuity and Laplace transformation o...This paper introduces some concepts such as q- process in random environment, Laplace transformation, ergodic potential kernel, error function and some basic lemmas.We study the continuity and Laplace transformation of random transition function. Finally, we give the sufficient condition for the existence of ergodic potential kernel for homogeneous q- processes in random environments.展开更多
The concepts of Markov process in random environment,q-matrix in random environment and q-process in random environment are introduced.Three forms of random Kolmoogrov farward(or backward)equations are introduced and ...The concepts of Markov process in random environment,q-matrix in random environment and q-process in random environment are introduced.Three forms of random Kolmoogrov farward(or backward)equations are introduced and the equivalence of these three forms are also proved.Moreover any conservative q-process in random environment satisfies random Kolmogrov backward equation.展开更多
In previous papers, the stationary distributions of a class of discrete and continuoustime random graph processes with state space consisting of the simple and directed graphs on Nvenices were studied. In this paper, ...In previous papers, the stationary distributions of a class of discrete and continuoustime random graph processes with state space consisting of the simple and directed graphs on Nvenices were studied. In this paper, the random graph graph process is extended one impotent stepfurther by allowing interaction of edges. Similarly, We obtha the expressions of the stationarydistributions and prove that the process is ergodic under different editions.展开更多
The representation of additive functionals and local times for jump Markov processes are obtained.The results of uniformly functional moderate deviation and their applications to birth-death processes are also presented.
We introduce some basic concepts such as random (sub-)transition function,q-function in random environment, q-process in random environment and some basic lemmas. For any continuous q-function in random environment, w...We introduce some basic concepts such as random (sub-)transition function,q-function in random environment, q-process in random environment and some basic lemmas. For any continuous q-function in random environment, we prove that the q-process in random environment always exists, and that any q-process in random environment satisfies the random Kolmogorov backward equation and the minimal q-process in random environment always exists. When q is a continuous and conservative q-function in random environment, the necessary and sufficient conditions for the uniqueness of q-process in random environment are given. Finally the special cases, homogeneous random transition functions and homogeneous q-processes in random environments are considered.展开更多
Let E be non-negative integer set Z+ or integer set Z. Q=（q<sub> </sub>: i, j∈E） is called a birth-and-death matrix if Q satisfies the following （ⅰ）—（ⅲ）: （ⅰ） q<sub> </sub>=0, |i-j|...Let E be non-negative integer set Z+ or integer set Z. Q=（q<sub> </sub>: i, j∈E） is called a birth-and-death matrix if Q satisfies the following （ⅰ）—（ⅲ）: （ⅰ） q<sub> </sub>=0, |i-j|】1, 0【q<sub> </sub>【+∞, |i-j|=1, （1） （ⅱ） sum from j≠i q<sub> </sub>≤q<sub>i</sub>≡-q<sub>ü</sub>≤+∞, （2） （ⅲ） if E=Z<sub>+</sub>, q<sub>i</sub>【+∞ and i≠0 or E=Z and q<sub>i</sub>【+∞ then q<sub>ü-1</sub>+q<sub>ü+1</sub> =q<sub>i</sub> （3） Let Q be a birth-and-death matrix. We call Q a birth-and-death matrix with展开更多
文摘The concepts of Markov process in random environment, q-matrix in random environment, and q-process in random environment are introduced. The minimal q-process in random environment is constructed and the necessary and sufficient conditions for the uniqueness of q-process in random environment are given.
基金the NNSF of China(10371092,10771185,10471148)the Foundation of Wuhan University
文摘This article is a continuation of[9].Based on the discussion of random Kolmogorov forward（backward）equations,for any given q-matrix in random environment, Q（θ）=（q（θ;x,y）,x,y∈X）,an infinite class of q-processes in random environments satisfying the random Kolmogorov forward（backward）equation is constructed.Moreover, under some conditions,all the q-processes in random environments satisfying the random Kolmogorov forward（backward）equation are constructed.
基金Supported by the National Natural Science Foundation of China (10371092)
文摘This paper introduces some concepts such as q- process in random environment, Laplace transformation, ergodic potential kernel, error function and some basic lemmas.We study the continuity and Laplace transformation of random transition function. Finally, we give the sufficient condition for the existence of ergodic potential kernel for homogeneous q- processes in random environments.
基金Supported by the National Natural Science Foun—dation of China(10371092 and 10171102)the Foundation of Wuhan University
文摘The concepts of Markov process in random environment,q-matrix in random environment and q-process in random environment are introduced.Three forms of random Kolmoogrov farward(or backward)equations are introduced and the equivalence of these three forms are also proved.Moreover any conservative q-process in random environment satisfies random Kolmogrov backward equation.
文摘In previous papers, the stationary distributions of a class of discrete and continuoustime random graph processes with state space consisting of the simple and directed graphs on Nvenices were studied. In this paper, the random graph graph process is extended one impotent stepfurther by allowing interaction of edges. Similarly, We obtha the expressions of the stationarydistributions and prove that the process is ergodic under different editions.
基金supported by the National Nature Science Foundation of China(10271091)
文摘The representation of additive functionals and local times for jump Markov processes are obtained.The results of uniformly functional moderate deviation and their applications to birth-death processes are also presented.
基金This work was supported by the National Natural Science Foundation of China(Grant No:10371092)the Foundation of Wuhan University.
文摘We introduce some basic concepts such as random (sub-)transition function,q-function in random environment, q-process in random environment and some basic lemmas. For any continuous q-function in random environment, we prove that the q-process in random environment always exists, and that any q-process in random environment satisfies the random Kolmogorov backward equation and the minimal q-process in random environment always exists. When q is a continuous and conservative q-function in random environment, the necessary and sufficient conditions for the uniqueness of q-process in random environment are given. Finally the special cases, homogeneous random transition functions and homogeneous q-processes in random environments are considered.
基金the National Natural Science Foundation of China.
文摘Let E be non-negative integer set Z+ or integer set Z. Q=（q<sub> </sub>: i, j∈E） is called a birth-and-death matrix if Q satisfies the following （ⅰ）—（ⅲ）: （ⅰ） q<sub> </sub>=0, |i-j|】1, 0【q<sub> </sub>【+∞, |i-j|=1, （1） （ⅱ） sum from j≠i q<sub> </sub>≤q<sub>i</sub>≡-q<sub>ü</sub>≤+∞, （2） （ⅲ） if E=Z<sub>+</sub>, q<sub>i</sub>【+∞ and i≠0 or E=Z and q<sub>i</sub>【+∞ then q<sub>ü-1</sub>+q<sub>ü+1</sub> =q<sub>i</sub> （3） Let Q be a birth-and-death matrix. We call Q a birth-and-death matrix with
