On the number of collisions in beta(2, b)-coalescents
Iksanov, Alex ; Marynych, Alex ; Möhle, Martin
Bernoulli, Tome 15 (2009) no. 1, p. 829-845 / Harvested from Project Euclid
Expansions are provided for the moments of the number of collisions Xn in the β(2, b)-coalescent restricted to the set {1, …, n}. We verify that $X_{n}/\mathbb{E}X_{n}$ converges almost surely to one and that Xn, properly normalized, weakly converges to the standard normal law. These results complement previously known facts concerning the number of collisions in β(a, b)-coalescents with a∈(0, 2) and b=1, and a>2 and b>0. The case a=2 is a kind of ‘border situation’ which seems not to be amenable to approaches used for a≠2.
Publié le : 2009-08-15
Classification:  asymptotics of moments,  beta-coalescent,  number of collisions,  random regenerative composition,  recursion with random indices
@article{1251463283,
     author = {Iksanov, Alex and Marynych, Alex and M\"ohle, Martin},
     title = {On the number of collisions in beta(2, b)-coalescents},
     journal = {Bernoulli},
     volume = {15},
     number = {1},
     year = {2009},
     pages = { 829-845},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1251463283}
}
Iksanov, Alex; Marynych, Alex; Möhle, Martin. On the number of collisions in beta(2, b)-coalescents. Bernoulli, Tome 15 (2009) no. 1, pp.  829-845. http://gdmltest.u-ga.fr/item/1251463283/