On the number of renewals in random time

Edward Omey , Georgi K. Mitov , Kosto V. Mitov

For the renewal counting process and the independent of it nonnegative random variable we investigate the asymptotic behaviour of and in case when the interarrival times have an infinite mean. These quantities appear in a natural way when considering limiting behaviour of random time changed branching processes and shock models.

Mots clés: 60K05; 60K99

Edward Omey, Georgi K. Mitov, Kosto V. Mitov. On the number of renewals in random time. Statistics and Probability Letters, 2009, 79 (21), pp.2281. ⟨10.1016/j.spl.2009.08.001⟩. ⟨hal-00582596⟩