Geodesic
The renewal equation with unbounded inhomogeneous term
Sibirskie èlektronnye matematičeskie izvestiâ, Tome 19 (2022) no. 1, pp. 81-90 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

We consider the renewal equation whose kernel is a probability distribution with positive mean. The inhomogeneous term behaves like a submultiplicative function tending to infinity. Asymptotic properties of the solution are established depending on the asymptotics of the submultiplicative function.
Keywords: renewal equation, probability distribution, positive mean, unbounded inhomogeneous term, submultiplicative function, asymptotic behavior. 
@article{SEMR_2022_19_1_a27,
     author = {M. S. Sgibnev},
     title = {The renewal equation with unbounded inhomogeneous term},
     journal = {Sibirskie \`elektronnye matemati\v{c}eskie izvesti\^a},
     pages = {81--90},
     year = {2022},
     volume = {19},
     number = {1},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SEMR_2022_19_1_a27/}
}
TY  - JOUR
AU  - M. S. Sgibnev
TI  - The renewal equation with unbounded inhomogeneous term
JO  - Sibirskie èlektronnye matematičeskie izvestiâ
PY  - 2022
SP  - 81
EP  - 90
VL  - 19
IS  - 1
UR  - http://geodesic.mathdoc.fr/item/SEMR_2022_19_1_a27/
LA  - en
ID  - SEMR_2022_19_1_a27
ER  - 
%0 Journal Article
%A M. S. Sgibnev
%T The renewal equation with unbounded inhomogeneous term
%J Sibirskie èlektronnye matematičeskie izvestiâ
%D 2022
%P 81-90
%V 19
%N 1
%U http://geodesic.mathdoc.fr/item/SEMR_2022_19_1_a27/
%G en
%F SEMR_2022_19_1_a27
M. S. Sgibnev. The renewal equation with unbounded inhomogeneous term. Sibirskie èlektronnye matematičeskie izvestiâ, Tome 19 (2022) no. 1, pp. 81-90. http://geodesic.mathdoc.fr/item/SEMR_2022_19_1_a27/

[1] W. Feller, An introduction to probability theory and its applications, v. II, Wiley, New York etc, 1966 | MR | Zbl

[2] E. Hille, R.S. Phillips, Functional analysis and semigroups, Colloquium Publications, 31, American Mathematical Society, Providence, 1957 | MR | Zbl

[3] G. Alsmeyer, Erneuerungstheorie, B.G. Teubner, Stuttgart, 1991 | MR | Zbl

[4] M.S. Sgibnev, “Stone's decomposition of the renewal measure via Banach-algebraic techniques”, Proc. Am. Math. Soc., 130:8 (2002), 2425–2430 | DOI | MR | Zbl

[5] M.S. Sgibnev, “An asymptotic expansion for the distribution of the supremum of a random walk”, Stud. Math., 140:1 (2000), 41–55 | DOI | MR | Zbl

[6] M.S. Sgibnev, “On invertibilty conditions for elements of Banach algebras of measures”, Math. Notes, 93:5 (2013), 763–765 | DOI | MR | Zbl

[7] W. Rudin, Principles of mathematical analysis, McGraw-Hill Book Company, New York etc, 1964 | MR | Zbl

[8] P.R. Halmos, Measure theory, Springer, New York etc, 1974 | MR | Zbl

[9] E. Seneta, Regularly varying functions, Springer, Berlin etc, 1976 | MR | Zbl

[10] M.S. Sgibnev, “The discrete renewal equation with nonsummable inhomogeneous term”, Brazilian Journal of Probability and Statistics (to appear) | MR