This paper is devoted to studying a new topic:optimal Markovian couplings,mainly for time-continuous Markov processes.The study emphasizes the analysis of the coupling opera- tors rather than the processes.Some constr...This paper is devoted to studying a new topic:optimal Markovian couplings,mainly for time-continuous Markov processes.The study emphasizes the analysis of the coupling opera- tors rather than the processes.Some constructions of optimal Markovian couplings for Markov chains and diffusions are presented,which are often unexpected.Then,the results are applied to study the L^2-convergence for Markov chains and for a diffusion on compact manifold.The estimate of the convergent rate provided by this method can be sharp.展开更多
In this paper,for two given transition probabilities,the existence of the optimal Markovian coupling with respect to a non-negative lower semi-continuous function is proved.As an application of this result,the well-kn...In this paper,for two given transition probabilities,the existence of the optimal Markovian coupling with respect to a non-negative lower semi-continuous function is proved.As an application of this result,the well-known Strassen’s theorem is generalized.Moreover,it is proved that the existence of an order-preserving Markovian coupling of two given jump processes is equivalent to their stochastical comparability.展开更多
In this work, by constructing optimal Markovian couplings we investigate exponential convergence rate in the Wasserstein distance for the transmission control protocol process. Most importantly, we provide a variation...In this work, by constructing optimal Markovian couplings we investigate exponential convergence rate in the Wasserstein distance for the transmission control protocol process. Most importantly, we provide a variational formula for the lower bound of the exponential convergence rate.展开更多
This paper is devoted to the investigation of stability for a class of coupled impulsive Markovian jump reaction-diffusion systems on networks(CIMJRDSNs). By using graph theory, a systematic method is provided to cons...This paper is devoted to the investigation of stability for a class of coupled impulsive Markovian jump reaction-diffusion systems on networks(CIMJRDSNs). By using graph theory, a systematic method is provided to construct global Lyapunov functions for the CIMJRDSNs. Based on Lyapunov functions and stochastic analysis method, some novel stability principles associated with the topology property of the networks are established.展开更多
基金Supported in part by NSFC,the State Education Commission of China,the NSERC operating grant of D.A.Dawson and Centro Vito Volterra.
文摘This paper is devoted to studying a new topic:optimal Markovian couplings,mainly for time-continuous Markov processes.The study emphasizes the analysis of the coupling opera- tors rather than the processes.Some constructions of optimal Markovian couplings for Markov chains and diffusions are presented,which are often unexpected.Then,the results are applied to study the L^2-convergence for Markov chains and for a diffusion on compact manifold.The estimate of the convergent rate provided by this method can be sharp.
基金Research supported in part by DPFIHE(Grant No.96002704)NNSFC(Grant No.19771008)
文摘In this paper,for two given transition probabilities,the existence of the optimal Markovian coupling with respect to a non-negative lower semi-continuous function is proved.As an application of this result,the well-known Strassen’s theorem is generalized.Moreover,it is proved that the existence of an order-preserving Markovian coupling of two given jump processes is equivalent to their stochastical comparability.
基金Supported NNSF of China(Grant Nos.11771327,2018JJ2478,11831014,12071340)。
文摘In this work, by constructing optimal Markovian couplings we investigate exponential convergence rate in the Wasserstein distance for the transmission control protocol process. Most importantly, we provide a variational formula for the lower bound of the exponential convergence rate.
基金supported by the National Natural Science Foundation of China under Grant Nos.61473097,11301090the State Key Program of Natural Science Foundation of China under Grant No.U1533202+2 种基金Shandong Independent Innovation and Achievements Transformation Fund under Grant No.2014CGZH1101Civil Aviation Administration of China under Grant No.MHRD20150104Guangxi Natural Science Foundation under Grant No.2016JJA110005
文摘This paper is devoted to the investigation of stability for a class of coupled impulsive Markovian jump reaction-diffusion systems on networks(CIMJRDSNs). By using graph theory, a systematic method is provided to construct global Lyapunov functions for the CIMJRDSNs. Based on Lyapunov functions and stochastic analysis method, some novel stability principles associated with the topology property of the networks are established.
