Large Deviations for Supercritical Multi-type Branching Processes

@inproceedings{Jones2001LargeDF,
  title={Large Deviations for Supercritical Multi-type Branching Processes},
  author={Owen Dafydd Jones},
  year={2001}
}
Large deviation results are obtained for the normed limit of a supercritical multi-type branching process. Starting from a single individual of type i, let L[i] be the normed limit of the branching process, and let Z k [i] be the minimum possible population size at generation k. If Z k [i] is bounded in k (bounded minimum growth) then we show that P(L[i] ≤ x) = P(L[i] = 0) + xF ∗[i](x) + o(x) as x → 0. If Z k [i] grows exponentially in k (exponential minimum growth) then we show that − log P(L… CONTINUE READING

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References

Publications referenced by this paper.
Showing 1-10 of 18 references

On the limit of a supercritical branching process

  • N. H. Bingham
  • J. Appl. Prob., 25A:215–228
  • 1988
Highly Influential
4 Excerpts

Asymptotic properties of supercritical age-dependent branching processes and homogeneous branching random walks

  • Q. Liu
  • Stoch. Proc. Appl., 82:61–87
  • 1999

Large deviation rates for supercritical and critical branching processes

  • K. B. Athreya, A. N. Vidyashankar
  • volume 84 of IMA Volumes in Math. and its Appl…
  • 1997

The growth of an entire characteristic function and tail probabilities of the limit of a tree martingale

  • Q. Liu
  • Prog. Prob., 40:51–80
  • 1996

Large deviation rates for branching processes II: The multitype case

  • K. B. Athreya, A. N. Vidyashankar
  • Ann. Appl. Prob., 5:566–576
  • 1995
1 Excerpt

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