On Stone’s renewal theorem for arithmetic distributions
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Mikhail S. Sgibnev
Abstract
The well-known Stone’s renewal theorem is refined for the case of arithmetic distributions having at least one exponentially decreasing tail. A very general version of the renewal theorem for arithmetic distributions with a semi-multiplicative bound of the residual term is proved.
Note: Originally published in Diskretnaya Matematika (2017) 29,№2, 84–95 (in Russian).
Acknowledgment
The author thanks the reviewer for careful reading the manuscript and helpful comments.
References
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© 2018 Walter de Gruyter GmbH, Berlin/Boston
Artikel in diesem Heft
- Frontmatter
- Estimate of the maximal cycle length in the graph of polynomial transformation of Galois–Eisenstein ring
- Durfee squares in compositions
- On fault detection tests of contact break for contact circuits
- On the number of integer points in a multidimensional domain
- On Stone’s renewal theorem for arithmetic distributions
- Local limit theorems for one class of distributions in probabilistic combinatorics
Artikel in diesem Heft
- Frontmatter
- Estimate of the maximal cycle length in the graph of polynomial transformation of Galois–Eisenstein ring
- Durfee squares in compositions
- On fault detection tests of contact break for contact circuits
- On the number of integer points in a multidimensional domain
- On Stone’s renewal theorem for arithmetic distributions
- Local limit theorems for one class of distributions in probabilistic combinatorics
