Precise large deviation for stationary sequence of branching process with immigration (2405.04835v1)

Published 8 May 2024 in math.PR

Abstract: 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.

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