11 papers
Coupling for one-dimensional subcritical and critical CBI processes with jumps
Shukai Chen, Chunhua Ma
We develop a cluster representation for one-dimensional CBI processes with jumps. Using this representation, we establish total variation convergence under conditions on the branch…
Mean-field branching SDEs: propagation of chaos, scaling limits and phase transitions
Shukai Chen, Lina Ji, Xiaowen Zhou
We study branching SDEs with law-dependent immigration and their mean-field particle approximations. Under a dissipativity condition and sufficiently weak interaction, a uniform pr…
Small value probabilities of additive and derivative martingales in supercritical branching Brownian motions and super Brownian motions
Shukai Chen, Haojie Hou
In this paper, we establish asymptotics for the small value probabilities of additive and derivative martingales in both supercritical branching Brownian motions and super Brownian…
A localized coupling approach to interacting continuous-state branching processes
Shukai Chen, Pei-Sen Li, Jian Wang
We introduce a class of continuous-state branching processes with immigration, predation and competition, which can be viewed as a combination of the classical Lotka-Volterra model…
Extinction, explosion and contraction for time-inhomogeneous SDEs with jumps
Shukai Chen, Xu Yang, Xiaowen Zhou
For a class of time-inhomogeneous SDEs with jumps, we establish criteria for the existence and uniqueness of the nonnegative solutions, and examine the extinction, the explosion to…
Exponential Ergodicity of CBIRE-Processes with Competition and Catastrophes
Shukai Chen, Rongjuan Fang, Lina Ji +1
We establish the exponential ergodic property in a weighted total variation distance of continuous-state branching processes with immigration in random environments with competitio…
Mixed state branching evolution for cell division models
Shukai Chen, Lina Ji, Jie Xiong
We prove a scaling limit theorem for two-type Galton-Waston branching processes with interaction. The limit theorem gives rise to a class of mixed state branching processes with in…
Moment properties for two-type continuous-state branching processes in random environments
Shukai Chen, Xiangqi Zheng
We first derive the recurisions for integer moments of two-type continuous-state branching processes in Lévy random environments. Result shows that the th moment of the process…
Wasserstein-type distances of two-type continuous-state branching processes in Lévy random environments
Shukai Chen, Rongjuan Fang, Xiangqi Zheng
Under natural conditions, we proved the exponential ergodicity in Wasserstein distance of two-type continuous-state branching processes in Lévy random environments with immigration…
Continuous Time Mixed State Branching Processes and Stochastic Equations
Shukai Chen, Zenghu Li
A continuous time mixed state branching process is constructed as the scaling limits of two-type Galton-Watson processes. The process can also be obtained by the pathwise unique so…
Ergodic and strong Feller properties of affine processes
Shukai Chen, Zenghu Li
For general (1+1)-affine Markov processes, we prove the ergodicity and exponential ergodicity in total variation distances. Our methods follow the arguments of ergodic properties f…