共查询到20条相似文献,搜索用时 15 毫秒
1.
Jeffrey S. Rosenthal 《Journal of Theoretical Probability》2003,16(3):671-688
We consider time-sampled Markov chain kernels, of the form P
=
n
n
P
n
. We prove bounds on the total variation distance to stationarity of such chains. We are motivated by the analysis of near-periodic MCMC algorithms. 相似文献
2.
给出齐次可列马尔科夫键转移矩阵的一种置换相似标准型,并用之来讨论键的极限性态,分别明确给出转移矩阵益收敛于零矩阵、非零矩阵、随机矩阵、常随机矩阵和正的常随机矩阵的充分必要条件. 相似文献
3.
将数列上的绝对平均收敛性推广到平面上,并得出相应的引理.利用这个概念给出非齐次马氏过程散度率存在的一个条件. 相似文献
4.
本主要讨论了依状态独立的随机环境中的马氏链,并严格地证明了依状态独立的随机环境中的马氏链,如果在环境不退化的一般情形下,不是时齐马氏链,而环境退化必然是马氏链这个结论。 相似文献
5.
引入了渐近循环马氏链的概念,它是循环马氏链概念的推广.首先研究了在强遍历的条件下,可列循环马氏链的收敛速度,作为主要结论给出了当满足不同条件时可列渐近循环马氏链的C-强遍历性,一致C-强遍历性和一致C-强遍历的收敛速度 相似文献
6.
Asymptotic properties of singularly perturbed Markov chains having measurable and/or continuous generators are developed in this work. The Markov chain under consideration has a finite-state space and is allowed to be nonstationary. Its generator consists of a rapidly varying part and a slowly changing part. The primary concerns are on the properties of the probability vectors and an aggregated process that depend on the characteristics of the fast varying part of the generators. The fast changing part of the generators can either consist of l recurrent classes, or include also transient states in addition to the recurrent classes. The case of inclusion of transient states is examined in detail. Convergence of the probability vectors under the weak topology of L2 is obtained first. Then under slightly stronger conditions, it is shown that the convergence also takes place pointwise. Moreover, convergence under the norm topology of L2 is derived. Furthermore, a process with aggregated states is obtained which converges to a Markov chain in distribution. 相似文献
7.
本提出了新的非齐次马尔可夫链的遍历条件,并在此条件下,首次证明了非齐次马尔可夫链转移概率的Gesaro-极限定理。另外,本还给出了一个例子,用它表明本的条件确实比Doeblin条件要弱。 相似文献
8.
This paper considers Markov chains on a locally compact separable metricspace, which have an invariant probability measure but with no otherassumption on the transition kernel. Within this context, the limit providedby several ergodic theorems is explicitly identified in terms of the limitof the expected occupation measures. We also extend Yosidasergodic decomposition for Feller-like kernels to arbitrarykernels, and present ergodic results for empirical occupation measures, aswell as for additive-noise systems. 相似文献
9.
利用鞅收敛定理讨论马氏环境中马氏链的强收敛性,建立相应的强大数定律,使得已知的一系列结果为其特例. 相似文献
10.
给出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新形式的强极限定理,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
11.
本文研究了马氏环境中的马氏链,利用马氏双链的性质,得到了马氏环境中的马氏链回返于小柱集上的概率的若干估计式. 相似文献
12.
13.
符方健 《数学的实践与认识》2010,40(20)
弱化Scott与Tweedie在计算马氏链收敛速度界时的条件,即变一步转移概率为m(m≥1)步转移概率,并运用不同于Scott与Tweedie的方法,计算出马氏链几何收敛速度r~n的界,从而推广了已有的结论. 相似文献
14.
The author presents a revised and detailed version of his theorem on the existence of Feller's extensions of Markov chains; to this end the broader notion of quasi-Feller extension is used. The existence of Markov chains dual to the chains with Borel space of states is derived from this result. Chains irreducible in the Orey sense are studied in most detail. For example, we prove that for such chains the quasi-Feller extension can be chosen recurrent or Liouville if the original chains possess these properties. 相似文献
15.
赵敏智 《数学年刊A辑(中文版)》2006,(6)
对零常返Markov链的首回速度进行了讨论.首先用n步转移概率{pxx(n)}刻画了Ex[w(τx)]有限的条件,这里τx是状态x的首回时,w是一个正函数.其次研究了与电网紧密联系的可逆Markov链,用一些有效电导给出点Ex[w,(τx)]有限的等价条件,并给出一些比较法则. 相似文献
16.
N. B. Yengibarian 《Journal of Theoretical Probability》2004,17(2):459-481
Existence of following factorization is proved:
Here A is a stochastic or semi-stochastic (substohastic) d×d matrix (d); I is the unit matrix; B and C are nonnegative, upper and lower triangular matrices. B is a semistochastic matrix; the diagonal entries of C are 1. An exact information on properties of matrices B and C are obtained in particular cases. Some results on existence of invariant distribution x for Markov chains in the cases of absence or presence of sources g of walking particles are obtained using the factorization (F). These problems described by homogeneous or nonhomogeneous equation (I–A)x=g. 相似文献
17.
讨论了具有离散参数的绕积马氏链的中心极限定理,给出了加在过程样本函数上充分条件。得到了绕积马氏链的中心极限定理成立的充分条件. 相似文献
18.
Aixin Tan Hani Doss James P. Hobert 《Journal of computational and graphical statistics》2013,22(3):792-826
Importance sampling is a classical Monte Carlo technique in which a random sample from one probability density, π1, is used to estimate an expectation with respect to another, π. The importance sampling estimator is strongly consistent and, as long as two simple moment conditions are satisfied, it obeys a central limit theorem (CLT). Moreover, there is a simple consistent estimator for the asymptotic variance in the CLT, which makes for routine computation of standard errors. Importance sampling can also be used in the Markov chain Monte Carlo (MCMC) context. Indeed, if the random sample from π1 is replaced by a Harris ergodic Markov chain with invariant density π1, then the resulting estimator remains strongly consistent. There is a price to be paid, however, as the computation of standard errors becomes more complicated. First, the two simple moment conditions that guarantee a CLT in the iid case are not enough in the MCMC context. Second, even when a CLT does hold, the asymptotic variance has a complex form and is difficult to estimate consistently. In this article, we explain how to use regenerative simulation to overcome these problems. Actually, we consider a more general setup, where we assume that Markov chain samples from several probability densities, π1, …, πk, are available. We construct multiple-chain importance sampling estimators for which we obtain a CLT based on regeneration. We show that if the Markov chains converge to their respective target distributions at a geometric rate, then under moment conditions similar to those required in the iid case, the MCMC-based importance sampling estimator obeys a CLT. Furthermore, because the CLT is based on a regenerative process, there is a simple consistent estimator of the asymptotic variance. We illustrate the method with two applications in Bayesian sensitivity analysis. The first concerns one-way random effect models under different priors. The second involves Bayesian variable selection in linear regression, and for this application, importance sampling based on multiple chains enables an empirical Bayes approach to variable selection. 相似文献
19.
20.
Kenneth S. Brown 《Journal of Theoretical Probability》2000,13(3):871-938
We analyze random walks on a class of semigroups called left-regular bands. These walks include the hyperplane chamber walks of Bidigare, Hanlon, and Rockmore. Using methods of ring theory, we show that the transition matrices are diagonalizable and we calculate the eigenvalues and multiplicities. The methods lead to explicit formulas for the projections onto the eigenspaces. As examples of these semigroup walks, we construct a random walk on the maximal chains of any distributive lattice, as well as two random walks associated with any matroid. The examples include a q-analogue of the Tsetlin library. The multiplicities of the eigenvalues in the matroid walks are generalized derangement numbers, which may be of independent interest. 相似文献