Precise large deviation for stationary sequence of branching process with immigration
- Resource Type
- Working Paper
- Authors
- Guo, Jiayan; Hong, Wenming
- Source
- Subject
- Mathematics - Probability
Primary 60J80, Secondary 60F10
- Language
It is known that there exists the stationary sequence of branching process with immigration $\{X_{n}\}_{n\in\mathbb{Z}}$ under some conditions (Foster and Williamson (1971)), when the offspring is critical or subcritical. A precise large deviation probability for the partial sum $S_{n}=X_{1}+\cdots+X_{n}$ is specified, the significant difference is revealed for the critical and subcritical cases.
Comment: arXiv admin note: substantial text overlap with arXiv:2405.04073