A nonhomogeneous Markov chain is applied to the study of the air quality classification in Mexico City when the so-called criterion pollutants are used. We consider the indices associated with air quality using two re...A nonhomogeneous Markov chain is applied to the study of the air quality classification in Mexico City when the so-called criterion pollutants are used. We consider the indices associated with air quality using two regulations where different ways of classification are taken into account. Parameters of the model are the initial and transition probabilities of the chain. They are estimated under the Bayesian point of view through samples generated directly from the corresponding posterior distributions. Using the estimated parameters, the probability of having an air quality index in a given hour of the day is obtained.展开更多
We investigate the convergence of nonhomogeneous Markov chains in general state space by using the f norm and the coupling method,and thus,a sufficient condition for the convergence of nonhomogeneous Markov chains in ...We investigate the convergence of nonhomogeneous Markov chains in general state space by using the f norm and the coupling method,and thus,a sufficient condition for the convergence of nonhomogeneous Markov chains in general state space is obtained.展开更多
The strong laws of large numbers for countable nonhomogeneous Markov chains have been discussed (cf. [1]—[3] ), where various restrictions were imposed on the Markov chains. The purpose of this report is to give a cl...The strong laws of large numbers for countable nonhomogeneous Markov chains have been discussed (cf. [1]—[3] ), where various restrictions were imposed on the Markov chains. The purpose of this report is to give a class of strong laws of large numbers which hold for arbitrary nonhomogeneous Markov chains. As corollaries of the main result, a relation between the relative frequency of occurrence of state couples and the transition probability of arbitrary nonhomogeneous Markov chains is established.展开更多
We model an epidemic with a class of nonhomogeneous Markov chains on the supercritical percolation network on Zd. The large deviations law for the Markov chain is given. Explicit expression of the rate function for la...We model an epidemic with a class of nonhomogeneous Markov chains on the supercritical percolation network on Zd. The large deviations law for the Markov chain is given. Explicit expression of the rate function for large deviation is obtained.展开更多
Let(ξ_n)_(n=0)~∞ be a Markov chain with the state space X = {1, 2, · · ·, b},(g_n(x, y))_(n=1)~∞ be functions defined on X × X, and F_(m_n,b_n)(ω) =1 /b_n sum from k=m_n+1 to m_n+b_n g_k(ξ_(k-...Let(ξ_n)_(n=0)~∞ be a Markov chain with the state space X = {1, 2, · · ·, b},(g_n(x, y))_(n=1)~∞ be functions defined on X × X, and F_(m_n,b_n)(ω) =1 /b_n sum from k=m_n+1 to m_n+b_n g_k(ξ_(k-1), ξ_k).In this paper the limit properties of F_(m_n,b_n)(ω) and the generalized relative entropy density f_(m_n,b_n)(ω) =-(1/b_n) log p(ξ_(m_n,m_n+b_n)) are discussed, and some theorems on a.s. convergence for(ξ_n)_n=0~∞ and the generalized Shannon-McMillan(AEP) theorem on finite nonhomogeneous Markov chains are obtained.展开更多
文摘A nonhomogeneous Markov chain is applied to the study of the air quality classification in Mexico City when the so-called criterion pollutants are used. We consider the indices associated with air quality using two regulations where different ways of classification are taken into account. Parameters of the model are the initial and transition probabilities of the chain. They are estimated under the Bayesian point of view through samples generated directly from the corresponding posterior distributions. Using the estimated parameters, the probability of having an air quality index in a given hour of the day is obtained.
基金Supported by Hubei Province Key Laboratory of Systems Science in Metallurgical Process(Wuhan University of Science and Technology)(Y202003)Hubei Education Department Foundation(B2019150)Natural Science Foundation of Xiaogan(XGKJ2020010046).
文摘We investigate the convergence of nonhomogeneous Markov chains in general state space by using the f norm and the coupling method,and thus,a sufficient condition for the convergence of nonhomogeneous Markov chains in general state space is obtained.
文摘The strong laws of large numbers for countable nonhomogeneous Markov chains have been discussed (cf. [1]—[3] ), where various restrictions were imposed on the Markov chains. The purpose of this report is to give a class of strong laws of large numbers which hold for arbitrary nonhomogeneous Markov chains. As corollaries of the main result, a relation between the relative frequency of occurrence of state couples and the transition probability of arbitrary nonhomogeneous Markov chains is established.
基金Supported by Mathematical Tianyuan Foundation （Grant No. 10926117） and National Natural Science Foundation of China （Grant No. 10531070） The authors would like to thank the referee for having read the paper carefully and for suggesting arrangements of article structure.
文摘We model an epidemic with a class of nonhomogeneous Markov chains on the supercritical percolation network on Zd. The large deviations law for the Markov chain is given. Explicit expression of the rate function for large deviation is obtained.
基金supported in part by the NNSF of China(No.11571142)the RP of Anhui Provincial Department of Education(No.KJ2017A851)
文摘Let(ξ_n)_(n=0)~∞ be a Markov chain with the state space X = {1, 2, · · ·, b},(g_n(x, y))_(n=1)~∞ be functions defined on X × X, and F_(m_n,b_n)(ω) =1 /b_n sum from k=m_n+1 to m_n+b_n g_k(ξ_(k-1), ξ_k).In this paper the limit properties of F_(m_n,b_n)(ω) and the generalized relative entropy density f_(m_n,b_n)(ω) =-(1/b_n) log p(ξ_(m_n,m_n+b_n)) are discussed, and some theorems on a.s. convergence for(ξ_n)_n=0~∞ and the generalized Shannon-McMillan(AEP) theorem on finite nonhomogeneous Markov chains are obtained.
