Skip to content

M.S. Sgibnev, Explicit formulas in renewal theory, Eur. J. Math. Appl. 4 (2024), Article ID 20.

Full Text: PDF

Volume 4 (2024), Article ID 20

https://doi.org/10.28919/ejma.2024.4.20

Published: 24/09/2024

Abstract:

Let $\{X_{i}\}$ be a sequence of independent identically distributed random variables with $\mathsf{E}X_{1}>0$. Let $\{S_{k}\}$ be the sequence of their partial sums and $U(\cdot)=\sum_{k=0}^{\infty}\mathsf{P}(S_{k}\in \cdot)$ be the corresponding renewal measure. We study the problem of representing in explicit form the restrictions of $U$ to the positive and negative half-axes. A similar problem for generalized renewal measures of special type is also considered.

How to Cite:

M.S. Sgibnev, Explicit formulas in renewal theory, Eur. J. Math. Appl. 4 (2024), Article ID 20. https://doi.org/10.28919/ejma.2024.4.20