In this paper,we consider a critical Galton-Watson branching process with immigration stopped at zero W.Some precise estimation on the probability generating function of the n-th population are obtained,and the tail p...In this paper,we consider a critical Galton-Watson branching process with immigration stopped at zero W.Some precise estimation on the probability generating function of the n-th population are obtained,and the tail probability of the life period of W is studied.Based on above results,two conditional limit theorems for W are established.展开更多
基金supported by China Postdoctoral Science Foundation(Grant No.2020M680269)National Natural Science Foundation of China(Grant No.12101023)+1 种基金the second author is supported by National Natural Science Foundation of China(Grant No.11871103)the National Key Research and Development Program of China(Grant No.2020YFA0712900)。
文摘In this paper,we consider a critical Galton-Watson branching process with immigration stopped at zero W.Some precise estimation on the probability generating function of the n-th population are obtained,and the tail probability of the life period of W is studied.Based on above results,two conditional limit theorems for W are established.
