Search results for "Markov renewal process"
showing 6 items of 6 documents
Statistics of transitions for Markov chains with periodic forcing
2013
The influence of a time-periodic forcing on stochastic processes can essentially be emphasized in the large time behaviour of their paths. The statistics of transition in a simple Markov chain model permits to quantify this influence. In particular the first Floquet multiplier of the associated generating function can be explicitly computed and related to the equilibrium probability measure of an associated process in higher dimension. An application to the stochastic resonance is presented.
ℓ1-Penalized Methods in High-Dimensional Gaussian Markov Random Fields
2016
In the last 20 years, we have witnessed the dramatic development of new data acquisition technologies allowing to collect massive amount of data with relatively low cost. is new feature leads Donoho to define the twenty-first century as the century of data. A major characteristic of this modern data set is that the number of measured variables is larger than the sample size; the word high-dimensional data analysis is referred to the statistical methods developed to make inference with this new kind of data. This chapter is devoted to the study of some of the most recent ℓ1-penalized methods proposed in the literature to make sparse inference in a Gaussian Markov random field (GMRF) defined …
Convergence of Markov Chains
2020
We consider a Markov chain X with invariant distribution π and investigate conditions under which the distribution of X n converges to π as n→∞. Essentially it is necessary and sufficient that the state space of the chain cannot be decomposed into subspaces that the chain does not leave, or that are visited by the chain periodically; e.g., only for odd n or only for even n.
Estimating finite mixtures of semi-Markov chains: an application to the segmentation of temporal sensory data
2019
Summary In food science, it is of great interest to obtain information about the temporal perception of aliments to create new products, to modify existing products or more generally to understand the mechanisms of perception. Temporal dominance of sensations is a technique to measure temporal perception which consists in choosing sequentially attributes describing a food product over tasting. This work introduces new statistical models based on finite mixtures of semi-Markov chains to describe data collected with the temporal dominance of sensations protocol, allowing different temporal perceptions for a same product within a population. The identifiability of the parameters of such mixtur…
ON HIGH-SKILL AND LOW-SKILL EQUILIBRIA: A MARKOV CHAIN APPROACH
2006
In this paper we propose to study the dynamics of human capital accumulation by means of a Markov chain. We identify the conditions for the emergence of ergodic and nonergodic dynamics, and relate them to various characteristics of an economic system. The model may generate high-skill and low-skill equilibria as well as intermediate situations. Policy implications are also discussed.
Juggler's exclusion process
2012
Juggler's exclusion process describes a system of particles on the positive integers where particles drift down to zero at unit speed. After a particle hits zero, it jumps into a randomly chosen unoccupied site. We model the system as a set-valued Markov process and show that the process is ergodic if the family of jump height distributions is uniformly integrable. In a special case where the particles jump according to a set-avoiding memoryless distribution, the process reaches its equilibrium in finite nonrandom time, and the equilibrium distribution can be represented as a Gibbs measure conforming to a linear gravitational potential.