Abstract
For the renewal counting process M ( t ) = min { k : S k > t } and the independent of it nonnegative random variable T , we investigate the asymptotic behaviour of P ( M ( t ) < T ) and P ( M ( t ) ≤ K ( t ) x ∣ M ( t ) < T ) in cases 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.
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