Search results for " Markov chain"
showing 10 items of 52 documents
The pianigiani-yorke measure for topological markov chains
1997
We prove the existence of a Pianigiani-Yorke measure for a Markovian factor of a topological Markov chain. This measure induces a Gibbs measure in the limit set. The proof uses the contraction properties of the Ruelle-Perron-Frobenius operator.
Context Trees, Variable Length Markov Chains and Dynamical Sources
2012
Infinite random sequences of letters can be viewed as stochastic chains or as strings produced by a source, in the sense of information theory. The relationship between Variable Length Markov Chains (VLMC) and probabilistic dynamical sources is studied. We establish a probabilistic frame for context trees and VLMC and we prove that any VLMC is a dynamical source for which we explicitly build the mapping. On two examples, the "comb" and the "bamboo blossom", we find a necessary and sufficient condition for the existence and the uniqueness of a stationary probability measure for the VLMC. These two examples are detailed in order to provide the associated Dirichlet series as well as the genera…
QUANTITATIVE CONVERGENCE RATES FOR SUBGEOMETRIC MARKOV CHAINS
2015
We provide explicit expressions for the constants involved in the characterisation of ergodicity of subgeometric Markov chains. The constants are determined in terms of those appearing in the assumed drift and one-step minorisation conditions. The results are fundamental for the study of some algorithms where uniform bounds for these constants are needed for a family of Markov kernels. Our results accommodate also some classes of inhomogeneous chains.
Space-time analysis of GDP disparities among European regions : a Markov chains approach
2004
The purpose of this paper is to study the evolution of the disparities between 138 European regions over the 1980-1995 period. We characterize the regional per capita GDP cross-sectional distribution by means of nonparametric estimations of density functions and we model the growth process as a first-order stationary Markov chain. Spatial effects are then introduced within the Markov chain framework using regional conditioning (Quah, 1996b) and spatial Markov chains (Rey, 2001). The results of the analysis indicate the persistence of regional disparities, a progressive bias toward a poverty trap and the importance of geography to explain the convergence process.
A study on forecasting electricity production and consumption in smart cities and factories
2019
Abstract The electrical power sector must undergo a thorough metamorphosis to achieve the ambitious targets in greenhouse gas reduction set forth in the Paris Agreement of 2015. Reducing uncertainty about demand and, in case of renewable electricity generation, supply is important for the determination of spot electricity prices. In this work we propose and evaluate a context-based technique to anticipate the electricity production and consumption in buildings. We focus on a household with photovoltaics and energy storage system. We analyze the efficiency of Markov chains, stride predictors and also their combination into a hybrid predictor in modelling the evolution of electricity producti…
Capacity Upper Bound of Channel Assembling in Cognitive Radio Networks with Quasistationary Primary User Activities
2013
In cognitive radio networks (CRNs) with multiple channels, various channel-assembling (ChA) strategies may be applied to secondary users (SUs), resulting in different achieved capacity. However, there is no previous work on determining the capacity upper bound (UB) of ChA for SUs under given system configurations. In this paper, we derive the maximum capacity for CRNs with ChA through Markov chain modeling, considering that primary user (PU) activities are relatively static, compared with SU services. We first deduce a closed-form expression for the maximum capacity in a dynamic ChA strategy and then demonstrate that no other ChA strategy can provide higher capacity than that achieved by th…
Aggregated Packet Transmission in Duty-Cycled WSNs: Modeling and Performance Evaluation
2017
[EN] Duty cycling (DC) is a popular technique for energy conservation in wireless sensor networks (WSNs) that allows nodes to wake up and sleep periodically. Typically, a single-packet transmission (SPT) occurs per cycle, leading to possibly long delay. With aggregated packet transmission (APT), nodes transmit a batch of packets in a single cycle. The potential benefits brought by an APT scheme include shorter delay, higher throughput, and higher energy efficiency. In the literature, different analytical models have been proposed to evaluate the performance of SPT schemes. However, no analytical models for the APT mode on synchronous DC medium access control (MAC) mechanisms exist. In this …
Uncommon Suffix Tries
2011
Common assumptions on the source producing the words inserted in a suffix trie with $n$ leaves lead to a $\log n$ height and saturation level. We provide an example of a suffix trie whose height increases faster than a power of $n$ and another one whose saturation level is negligible with respect to $\log n$. Both are built from VLMC (Variable Length Markov Chain) probabilistic sources; they are easily extended to families of sources having the same properties. The first example corresponds to a ''logarithmic infinite comb'' and enjoys a non uniform polynomial mixing. The second one corresponds to a ''factorial infinite comb'' for which mixing is uniform and exponential.
Adaptive independent sticky MCMC algorithms
2018
In this work, we introduce a novel class of adaptive Monte Carlo methods, called adaptive independent sticky MCMC algorithms, for efficient sampling from a generic target probability density function (pdf). The new class of algorithms employs adaptive non-parametric proposal densities which become closer and closer to the target as the number of iterations increases. The proposal pdf is built using interpolation procedures based on a set of support points which is constructed iteratively based on previously drawn samples. The algorithm's efficiency is ensured by a test that controls the evolution of the set of support points. This extra stage controls the computational cost and the converge…
Conditional particle filters with diffuse initial distributions
2020
Conditional particle filters (CPFs) are powerful smoothing algorithms for general nonlinear/non-Gaussian hidden Markov models. However, CPFs can be inefficient or difficult to apply with diffuse initial distributions, which are common in statistical applications. We propose a simple but generally applicable auxiliary variable method, which can be used together with the CPF in order to perform efficient inference with diffuse initial distributions. The method only requires simulatable Markov transitions that are reversible with respect to the initial distribution, which can be improper. We focus in particular on random-walk type transitions which are reversible with respect to a uniform init…