%A 陈舒凯, 李增沪 %T CONTINUOUS TIME MIXED STATE BRANCHING PROCESSES AND STOCHASTIC EQUATIONS %0 Journal Article %D 2021 %J 数学物理学报(英文版) %R 10.1007/s10473-021-0504-7 %P 1445-1473 %V 41 %N 5 %U {http://121.43.60.238/sxwlxbB/CN/abstract/article_16514.shtml} %8 2021-10-25 %X A continuous time and mixed state branching process is constructed by a scaling limit theorem of two-type Galton-Watson processes. The process can also be obtained by the pathwise unique solution to a stochastic equation system. From the stochastic equation system we derive the distribution of local jumps and give the exponential ergodicity in Wasserstein-type distances of the transition semigroup. Meanwhile, we study immigration structures associated with the process and prove the existence of the stationary distribution of the process with immigration.