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Equivalent conditions of local asymptotics for the solutions of defective renewal equations, with applications. (English) Zbl 1200.60073

Summary: The paper obtains some equivalent conditions of local asymptotics for the solutions of defective renewal equations in the heavy-tailed case. As applications, the paper gives a different proof of a classical result about the local distribution of the supremum of a random walk. These results are also applied in examples involving the renewal function for terminating renewal processes and the age-dependent branching processes.

MSC:

60K05 Renewal theory
60K10 Applications of renewal theory (reliability, demand theory, etc.)
60K30 Applications of queueing theory (congestion, allocation, storage, traffic, etc.)
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