Abstract
Consider some renewal sequence, that is, a sequence of partial sums {S n}n≥0 of independent identically distributed random variables {X n}n≥1. Our aim in this chapter is to show that various functionals of partial sums and corresponding renewal processes are asymptotically equivalent if one considers them from the point of view of generalized renewal processes.
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Buldygin, V.V., Indlekofer, KH., Klesov, O.I., Steinebach, J.G. (2018). Almost Sure Convergence of Renewal Processes. In: Pseudo-Regularly Varying Functions and Generalized Renewal Processes. Probability Theory and Stochastic Modelling, vol 91. Springer, Cham. https://doi.org/10.1007/978-3-319-99537-3_2
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