Lundberg inequalities for renewal equations (Q2759815)

Sharp upper and lower bounds are derived for the solution to the renewal equation, which arises in a wide variety of applied probability models. These include exponential bounds for specific cases. In the case of defective renewal equation non-exponential bounds are obtained. The exact nature of these bounds depends on reliability properties and classifications. Applications of these results in examples involving the severity of insurance ruin, age-dependent branching processes, and a generalized type II Geiger counter are also given.