共查询到20条相似文献,搜索用时 15 毫秒
1.
This work is concerned with asymptotic properties of Markov-modulated random processes having two timescales. The model contains a number of mixing sequences modulated by a switching process that is a discrete-time Markov chain. The motivation of our study stems from applications in manufacturing systems, communication networks and economic systems, in which regime-switching models are used. This paper focuses on asymptotic properties of the Markov-modulated processes under suitable scaling. Our main effort focuses on obtaining a strong approximation result. 相似文献
2.
3.
4.
5.
6.
《Expositiones Mathematicae》2019,37(1):96-102
We give a simple proof of Tutte’s matrix-tree theorem, a well-known result providing a closed-form expression for the number of rooted spanning trees in a directed graph. Our proof stems from placing a random walk on a directed graph and then applying the Markov chain tree theorem to count trees. The connection between the two theorems is not new, but it appears that only one direction of the formal equivalence between them is readily available in the literature. The proof we now provide establishes the other direction. More generally, our approach is another example showing that random walks can serve as a powerful glue between graph theory and Markov chain theory, allowing formal statements from one side to be carried over to the other. 相似文献
7.
This work is concerned with weak convergence of non-Markov random processes modulated by a Markov chain. The motivation of our study stems from a wide variety of applications in actuarial science, communication networks, production planning, manufacturing and financial engineering. Owing to various modelling considerations, the modulating Markov chain often has a large state space. Aiming at reduction of computational complexity, a two-time-scale formulation is used. Under this setup, the Markov chain belongs to the class of nearly completely decomposable class, where the state space is split into several subspaces. Within each subspace, the transitions of the Markov chain varies rapidly, and among different subspaces, the Markov chain moves relatively infrequently. Aggregating all the states of the Markov chain in each subspace to a single super state leads to a new process. It is shown that under such aggregation schemes, a suitably scaled random sequence converges to a switching diffusion process. 相似文献
8.
Yuliang Han 《Journal of Mathematical Analysis and Applications》2007,336(2):962-974
In this paper almost periodic random sequence in probability is defined and investigated. It is also applied to random difference equations by means of exponential dichotomy. The existence of such kind of solutions of random difference equations is discussed. 相似文献
9.
C. Boldrighini R. A. Minlos A. Pellegrinotti 《Probability Theory and Related Fields》1997,109(2):245-273
Summary We consider a model of random walk on ℤν, ν≥2, in a dynamical random environment described by a field ξ={ξ
t
(x): (t,x)∈ℤν+1}. The random walk transition probabilities are taken as P(X
t
+1= y|X
t
= x,ξ
t
=η) =P
0( y−x)+ c(y−x;η(x)). We assume that the variables {ξ
t
(x):(t,x) ∈ℤν+1} are i.i.d., that both P
0(u) and c(u;s) are finite range in u, and that the random term c(u;·) is small and with zero average. We prove that the C.L.T. holds almost-surely, with the same parameters as for P
0, for all ν≥2. For ν≥3 there is a finite random (i.e., dependent on ξ) correction to the average of X
t
, and there is a corresponding random correction of order to the C.L.T.. For ν≥5 there is a finite random correction to the covariance matrix of X
t
and a corresponding correction of order to the C.L.T.. Proofs are based on some new L
p
estimates for a class of functionals of the field.
Received: 4 January 1996/In revised form: 26 May 1997 相似文献
10.
Asymptotic distribution of the numbers of vertices and arcs of the giant strong component in sparse random digraphs 下载免费PDF全文
Two models of a random digraph on n vertices, and are studied. In 1990, Karp for D(n, p) and independently T. ?uczak for D(n,m = cn) proved that for c > 1, with probability tending to 1, there is an unique strong component of size of order n. Karp showed, in fact, that the giant component has likely size asymptotic to nθ2, where θ = θ(c) is the unique positive root of . In this paper we prove that, for both random digraphs, the joint distribution of the number of vertices and number of arcs in the giant strong component is asymptotically Gaussian with the same mean vector , and two distinct 2 × 2 covariance matrices, and . To this end, we introduce and analyze a randomized deletion process which terminates at the directed (1, 1)‐core, the maximal digraph with minimum in‐degree and out‐degree at least 1. This (1, 1)‐core contains all non‐trivial strong components. However, we show that the likely numbers of peripheral vertices and arcs in the (1, 1)‐core, those outside the largest strong component, are of polylog order, thus dwarfed by anticipated fluctuations, on the scale of n1/2, of the giant component parameters. By approximating the likely realization of the deletion algorithm with a deterministic trajectory, we obtain our main result via exponential supermartingales and Fourier‐based techniques. © 2015 Wiley Periodicals, Inc. Random Struct. Alg., 49, 3–64, 2016 相似文献
11.
Let M n denote the partial maximum of a strictly stationary sequence (X n ). Suppose that some of the random variables of (X n ) can be observed and let [(M)tilde]ntilde M_n stand for the maximum of observed random variables from the set {X 1, ..., X n }. In this paper, the almost sure limit theorems related to random vector ([(M)tilde]ntilde M_n , M n ) are considered in terms of i.i.d. case. The related results are also extended to weakly dependent stationary Gaussian sequence as its covariance function satisfies some regular conditions. 相似文献
12.
Yu Quan Xie 《数学学报(英文版)》2008,24(12):1965-1984
In this paper, we study the basic properties of stationary transition probability of Markov processes on a general measurable space (E, δ), such as the continuity, maximum probability, zero point, positive probability set,standardization, and obtain a series of important results such as Continuity Theorem, Representation Theorem, Levy Theorem and so on. These results are very useful for us to study stationary tri-point transition probability on a general measurable space (E, δ). Our main tools such as Egoroff's Theorem, Vitali-Hahn-Saks's Theorem and the theory of atomic set and well- posedness of measure are also very interesting and fashionable. 相似文献
13.
研究了以转移概率矩阵评价教学效果的两种方法:Markov链模型和罚因子法;特别是在第二种方法中,通过一个非常简单的"罚因子",可以迅速得到结论.利用这两种方法,有效的提高了教学评估的科学性,并且将这两种方法的适用范围加以推广. 相似文献
14.
刘文 《应用数学学报(英文版)》1996,12(3):328-331
ASTRONGLIMITTHEOREMFORGENERALIZEDCANTOR-LIKE RANDOM SEQUENCESLIUWEN(刘文)(DepartmentofMathematicsandPhysics,HebeiUniversityofTe... 相似文献
15.
金少华 《数学的实践与认识》2007,37(13):118-123
给出了一个关于可列非齐次马尔可夫链M元状态序组出现频率的一个强极限定理及其推广,所得结论对任意可列非齐次马尔可夫链普遍成立. 相似文献
16.
In this paper, we prove a local limit theorem for the distribution of the number of triangles in the Erdos‐Rényi random graph G(n, p), where is a fixed constant. Our proof is based on bounding the characteristic function of the number of triangles, and uses several different conditioning arguments for handling different ranges of t. © 2016 Wiley Periodicals, Inc. Random Struct. Alg., 48, 732–750, 2016 相似文献
17.
We analyze the (3, 2, 1)‐Shell Sort algorithm under the usual random permutation model. © 2002 Wiley Periodicals, Inc. Random Struct. Alg., 21: 59–75, 2002 相似文献
18.
无规则性概念在马尔科夫链中的推广 总被引:2,自引:0,他引:2
概率论中无规则性概念的基本思想是,在取0与1的两个等可能值的Bernoulli序列中,0和1的出现是完全无规则的,而且想要通过选择来控制它稍偏多于0或1也是不可能的.本文的目的是要建立一类与马尔科夫链有关的极限定理,其中包合无规则性概念的推广. 相似文献
19.
20.
Andrei Novikov 《Annals of the Institute of Statistical Mathematics》2001,53(4):799-809
An asymptotic expansion of the logarithm of the likelihood ratio for Markov dependent observation is obtained. A functional limit theorem for the likelihood ratio is proved, which gives a way to study limiting distributions of the likelihood ratio based on stopping times, in particular, that of sequential probability ratio test. 相似文献