MA Chunhua, . A Fluctuation Limit Theorem of Branching Processes with Immigration and Statistical Applications[J]. Chinese Journal of Applied Probability and Statistics, 2022, 38(3): 454-474.
Citation: MA Chunhua, . A Fluctuation Limit Theorem of Branching Processes with Immigration and Statistical Applications[J]. Chinese Journal of Applied Probability and Statistics, 2022, 38(3): 454-474.

A Fluctuation Limit Theorem of Branching Processes with Immigration and Statistical Applications

  • We prove a general fluctuation limit theorem for Galton-Watson branching processes with immigration. The limit is a time-inhomogeneous OU type process driven by a spectrally positive L\'evy process. As applications of this result, we obtain some asymptotic estimates for the conditional least squares estimators of the means of the offspring and immigration distributions.
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