This work is devoted to stochastic systems arising from empirical measures of random sequences(termed primary sequences) that are modulated by another Markov chain. The Markov chain is used to model random discrete ev...This work is devoted to stochastic systems arising from empirical measures of random sequences(termed primary sequences) that are modulated by another Markov chain. The Markov chain is used to model random discrete events that are not represented in the primary sequences. One novel feature is that in lieu of the usual scaling in empirical measure sequences, the authors consider scaling in both space and time, which leads to new limit results. Under broad conditions, it is shown that a scaled sequence of the empirical measure converges weakly to a number of Brownian bridges modulated by a continuous-time Markov chain. Ramifications and special cases are also considered.展开更多
Abstract The authors prove an almost sure central limit theorem for partial sums based on an irreducible and positive recurrent Markov chain using logarithmic means, which realizes the extension of the almost sure cen...Abstract The authors prove an almost sure central limit theorem for partial sums based on an irreducible and positive recurrent Markov chain using logarithmic means, which realizes the extension of the almost sure central limit theorem for partial sums from an i.i.d, sequence of random variables to a Markov chain.展开更多
In this paper, the continuous-time independent edge-Markovian random graph process model is constructed. The authors also define the interval isolated nodes of the random graph process, study the distribution sequence...In this paper, the continuous-time independent edge-Markovian random graph process model is constructed. The authors also define the interval isolated nodes of the random graph process, study the distribution sequence of the number of isolated nodes and the probability of having no isolated nodes when the initial distribution of the random graph process is stationary distribution, derive the lower limit of the probability in which two arbitrary nodes are connected and the random graph is also connected, and prove that the random graph is almost everywhere connected when the number of nodes is sufficiently large.展开更多
基金supported by the Air Force Office of Scientific Research under Grant No.FA9550-15-1-0131
文摘This work is devoted to stochastic systems arising from empirical measures of random sequences(termed primary sequences) that are modulated by another Markov chain. The Markov chain is used to model random discrete events that are not represented in the primary sequences. One novel feature is that in lieu of the usual scaling in empirical measure sequences, the authors consider scaling in both space and time, which leads to new limit results. Under broad conditions, it is shown that a scaled sequence of the empirical measure converges weakly to a number of Brownian bridges modulated by a continuous-time Markov chain. Ramifications and special cases are also considered.
基金supported by the National Natural Science Foundation of China (No. 11171275)the Program for Excellent Talents in Chongqing Higher Education Institutions (No. 120060-20600204)Liaocheng University Foundation (No. X09005)
文摘Abstract The authors prove an almost sure central limit theorem for partial sums based on an irreducible and positive recurrent Markov chain using logarithmic means, which realizes the extension of the almost sure central limit theorem for partial sums from an i.i.d, sequence of random variables to a Markov chain.
基金supported by the National Natural Science Foundation of China(Nos.60872060,11101265)the Shanghai Natural Science Foundation of China(No.12ZR1421000)the Shanghai Education Commission Innovation Project Fund(Nos.12ZZ193,14YZ152,15ZZ099)
文摘In this paper, the continuous-time independent edge-Markovian random graph process model is constructed. The authors also define the interval isolated nodes of the random graph process, study the distribution sequence of the number of isolated nodes and the probability of having no isolated nodes when the initial distribution of the random graph process is stationary distribution, derive the lower limit of the probability in which two arbitrary nodes are connected and the random graph is also connected, and prove that the random graph is almost everywhere connected when the number of nodes is sufficiently large.
