Upper deviation results are obtained for the split time of a supercritical continuous-time Markov branching process. More precisely, we establish the existence of logarithmic limits for the likelihood that the split times of the process are greater than an identified value and determine an expression for the limiting quantity. We also give an estimation for the lower deviation probability of the split times, which shows that the scaling is completely different from the upper deviations.
- Continuous-time branching process
- Large deviation
- Split time
ASJC Scopus subject areas
- Statistics and Probability
- Statistics, Probability and Uncertainty