Harmonic Moments for Supercritical Multi-type Galton–Watson Processes
Jiangrui Tan , Mei Zhang
Frontiers of Mathematics ›› : 1 -26.
Harmonic Moments for Supercritical Multi-type Galton–Watson Processes
In this paper, the convergence rates of harmonic moment E[(1 · Zn)−r] of a supercritical multi-type Galton–Watson process {Zn; n ≥ 0} are studied. It is shown that there exists a phase transition in the convergence rate of the harmonic moments, which extends the results from single type cases to multi-type cases. Based on above result, under some moment hypothesis on Zn, the large deviations of $\boldsymbol{l} \cdot \boldsymbol{Z}_{n+1}\over \boldsymbol{1}\cdot\boldsymbol{Z}_{n}$ are studied for l > 0. In particular, in the case that the offspring distributions are of Pareto-type, an explicit large deviation result is obtained.
Supercritical / multi-type / Galton–Watson processes / harmonic moments / large deviations
/
| 〈 |
|
〉 |