The Experts below are selected from a list of 53283 Experts worldwide ranked by ideXlab platform
Weiguo Yang - One of the best experts on this subject based on the ideXlab platform.
-
the generalized entropy ergodic theorem for nonhomogeneous Markov Chains
Journal of Theoretical Probability, 2016Co-Authors: Zhongzhi Wang, Weiguo YangAbstract:Let \((\xi _n)_{n=0}^\infty \) be a nonhomogeneous Markov chain taking values in a finite state-space \(\mathbf {X}=\{1,2,\ldots ,b\}\). In this paper, we will study the generalized entropy ergodic theorem with almost-everywhere and \(\mathcal {L}_1\) convergence for nonhomogeneous Markov Chains; this generalizes the corresponding classical results for Markov Chains.
-
the generalized entropy ergodic theorem for nonhomogeneous Markov Chains
arXiv: Probability, 2015Co-Authors: Zhongzhi Wang, Weiguo YangAbstract:Let $(\xi_n)_{n=0}^\infty$ be a nonhomogeneous Markov chain taking values from finite state-space of $\mathbf{X}=\{1,2,\ldots,b\}$. In this paper, we will study the generalized entropy ergodic theorem with almost-everywhere and $\mathcal{L}_1$ convergence for nonhomogeneous Markov Chains, which generalizes the corresponding classical results for the Markov Chains.
-
the asymptotic equipartition property for asymptotic circular Markov Chains
Probability in the Engineering and Informational Sciences, 2010Co-Authors: Pingping Zhong, Weiguo Yang, Peipei LiangAbstract:In this article, we study the asymptotic equipartition property (AEP) for asymptotic circular Markov Chains. First, the definition of an asymptotic circular Markov chain is introduced. Then by applying the limit property for the bivariate functions of nonhomogeneous Markov Chains, the strong limit theorem on the frequencies of occurrence of states for asymptotic circular Markov Chains is established. Next, the strong law of large numbers on the frequencies of occurrence of states for asymptotic circular Markov Chains is obtained. Finally, we prove the AEP for asymptotic circular Markov Chains.
-
the asymptotic equipartition property for nonhomogeneous Markov Chains indexed by a homogeneous tree
IEEE Transactions on Information Theory, 2007Co-Authors: Weiguo YangAbstract:In this correspondence, we first establish a strong limit theorem for countable nonhomogeneous Markov Chains indexed by a homogeneous tree. As corollaries, we obtain some strong limit theorems for frequencies of occurrence of states and ordered couple of states for these Markov Chains. Finally, we prove the strong law of large numbers and the asymptotic equipartition property (AEP) for finite nonhomogeneous Markov Chains indexed by a homogeneous tree.
Abraham J Wyner - One of the best experts on this subject based on the ideXlab platform.
-
variable length Markov Chains
Annals of Statistics, 1999Co-Authors: Peter Buhlmann, Abraham J WynerAbstract:We study estimation in the class of stationary variable length Markov Chains (VLMC) on a finite space. The processes in this class are still Markovian of high order, but with memory of variable length yielding a much bigger and structurally richer class of models than ordinary high-order Markov Chains. From an algorithmic view, the VLMC model class has attracted interest in information theory and machine learning, but statistical properties have not yet been explored. Provided that good estimation is available, the additional structural richness of the model class enhances predictive power by finding a better trade-off between model bias and variance and allowing better structural description which can be of specific interest. The latter is exemplified with some DNA data. A version of the tree-structured context algorithm, proposed by Rissanen in an information theoretical set-up is shown to have new good asymptotic properties for estimation in the class of VLMCs. This remains true even when the underlying model increases in dimensionality. Furthermore, consistent estimation of minimal state spaces and mixing properties of fitted models are given. We also propose a new bootstrap scheme based on fitted VLMCs. We show its validity for quite general stationary categorical time series and for a broad range of statistical procedures.
Robert K Brayton - One of the best experts on this subject based on the ideXlab platform.
-
model checking continuous time Markov Chains
ACM Transactions on Computational Logic (TOCL), 2000Co-Authors: Adnan Aziz, Kumud K Sanwal, Vigyan Singhal, Robert K BraytonAbstract:We present a logical formalism for expressing properties of continuous-time Markov Chains. The semantics for such properties arise as a natural extension of previous work on discrete-time Markov Chains to continuous time. The major result is that the verification problem is decidable; this is shown using results in algebraic and transcendental number theory.
-
verifying continuous time Markov Chains
Computer Aided Verification, 1996Co-Authors: Adnan Aziz, Kumud K Sanwal, Vigyan Singhal, Robert K BraytonAbstract:We present a logical formalism for expressing properties of continuous time Markov Chains. The semantics for such properties arise as a natural extension of previous work on discrete time Markov Chains to continuous time. The major result is that the verification problem is decidable; this is shown using results in algebraic and transcendental number theory.
Jan Maas - One of the best experts on this subject based on the ideXlab platform.
-
ricci curvature of finite Markov Chains via convexity of the entropy
Archive for Rational Mechanics and Analysis, 2012Co-Authors: Matthias Erbar, Jan MaasAbstract:We study a new notion of Ricci curvature that applies to Markov Chains on discrete spaces. This notion relies on geodesic convexity of the entropy and is analogous to the one introduced by Lott, Sturm, and Villani for geodesic measure spaces. In order to apply to the discrete setting, the role of the Wasserstein metric is taken over by a different metric, having the property that continuous time Markov Chains are gradient flows of the entropy. Using this notion of Ricci curvature we prove discrete analogues of fundamental results by Bakry–Emery and Otto–Villani. Further, we show that Ricci curvature bounds are preserved under tensorisation. As a special case we obtain the sharp Ricci curvature lower bound for the discrete hypercube.
-
ricci curvature of finite Markov Chains via convexity of the entropy
arXiv: Metric Geometry, 2011Co-Authors: Matthias Erbar, Jan MaasAbstract:We study a new notion of Ricci curvature that applies to Markov Chains on discrete spaces. This notion relies on geodesic convexity of the entropy and is analogous to the one introduced by Lott, Sturm, and Villani for geodesic measure spaces. In order to apply to the discrete setting, the role of the Wasserstein metric is taken over by a different metric, having the property that continuous time Markov Chains are gradient flows of the entropy. Using this notion of Ricci curvature we prove discrete analogues of fundamental results by Bakry--Emery and Otto--Villani. Furthermore we show that Ricci curvature bounds are preserved under tensorisation. As a special case we obtain the sharp Ricci curvature lower bound for the discrete hypercube.
Francois Dufour - One of the best experts on this subject based on the ideXlab platform.
-
invariant probability measures for a class of feller Markov Chains
Statistics & Probability Letters, 2000Co-Authors: O L V Costa, Francois DufourAbstract:Abstract In this paper we consider a Markov chain defined on a locally compact separable metric space which satisfies the Feller property. We introduce a new assumption which generalizes T-chain and irreducibility assumptions, well known in the literature of Markov Chains. Under this new assumption, the Foster's criterion is shown to be equivalent to the existence of an invariant probability measure for Feller–Markov Chains, which is also equivalent to the existence of a non-singular invariant probability measure.
