Limit Theorems for Renewal Processes
نویسندگان
چکیده
This article describes the Key renewal theorem and the Blackwell’s renewaltheorem. These two limit theorems for renewal processes are equivalent but of different forms.They are particularly useful for characterizing the asymptotic behavior of a probabilisticquantity of interest in a renewal process. We present two applications of these limit theorems:the limiting distributions of recurrence times in a renewal process and the asymptotic expansionof a renewal function. Further readings on the theoretical development of these limit theoremsand their applications in different areas are also provided.
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