Abstract
We consider critical branching Bessel processes initially at $r \gg 1$ and stopped at $r = 1$. Let $N$ be the number of descendants hitting $r = 1$. We give the norming constant $k(r)$ and prove convergence, as $r \rightarrow \infty$, of $N/\lbrack k(r) \rbrack$ conditioned on $\{N > 0\}$. The distribution of conditioned limit laws is also investigated. A feature of this study is an interplay between probabilistic insights and analytic techniques for Emden-Fowler's equation.
Citation
Tzong-Yow Lee. "Conditioned Limit Theorems of Stopped Critical Branching Bessel Processes." Ann. Probab. 18 (1) 272 - 289, January, 1990. https://doi.org/10.1214/aop/1176990949
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