Based on an explicit representation of moments of hitting times for single death processes, the criteria on ergodicity and strong ergodicity are obtained. These results can be applied for an extended class of branchin...Based on an explicit representation of moments of hitting times for single death processes, the criteria on ergodicity and strong ergodicity are obtained. These results can be applied for an extended class of branching processes. Meanwhile, some sufficient and necessary conditions for recurrence and exponential ergodicity as well as extinction probability for the processes are presented.展开更多
Abstract Let P be a transition matrix which is symmetric with respect to a measure π. The spectral gap of P in L2（π）-space, denoted by gap（P）, is defined as the distance between 1 and the rest of the spectrum of...Abstract Let P be a transition matrix which is symmetric with respect to a measure π. The spectral gap of P in L2（π）-space, denoted by gap（P）, is defined as the distance between 1 and the rest of the spectrum of P. In this paper, we study the relationship between gap（P） and the convergence rate of P^n. When P is transient, the convergence rate of pn is equal to 1 - gap（P）. When P is ergodic, we give the explicit upper and lower bounds for the convergence rate of pn in terms of gap（P）. These results are extended to L^∞ （π）-space.展开更多
The nonlinear branching process with immigration is constructed as the pathwise unique solution of a stochastic integral equation driven by Poisson random measures. Some criteria for the regularity, recurrence, ergodi...The nonlinear branching process with immigration is constructed as the pathwise unique solution of a stochastic integral equation driven by Poisson random measures. Some criteria for the regularity, recurrence, ergodicity and strong ergodicity of the process are then established.展开更多
文摘Based on an explicit representation of moments of hitting times for single death processes, the criteria on ergodicity and strong ergodicity are obtained. These results can be applied for an extended class of branching processes. Meanwhile, some sufficient and necessary conditions for recurrence and exponential ergodicity as well as extinction probability for the processes are presented.
基金Supported in part by 985 Project,973 Project(Grant No.2011CB808000)National Natural Science Foundation of China(Grant No.11131003)+1 种基金Specialized Research Fund for the Doctoral Program of Higher Education(Grant No.20100003110005)the Fundamental Research Funds for the Central Universities
文摘Abstract Let P be a transition matrix which is symmetric with respect to a measure π. The spectral gap of P in L2（π）-space, denoted by gap（P）, is defined as the distance between 1 and the rest of the spectrum of P. In this paper, we study the relationship between gap（P） and the convergence rate of P^n. When P is transient, the convergence rate of pn is equal to 1 - gap（P）. When P is ergodic, we give the explicit upper and lower bounds for the convergence rate of pn in terms of gap（P）. These results are extended to L^∞ （π）-space.
基金Supported by NSFC(Grant Nos.1131003,11626245 and 11571043)
文摘The nonlinear branching process with immigration is constructed as the pathwise unique solution of a stochastic integral equation driven by Poisson random measures. Some criteria for the regularity, recurrence, ergodicity and strong ergodicity of the process are then established.
