Geodesic
The renewal equation with unbounded inhomogeneous term
Sibirskie èlektronnye matematičeskie izvestiâ, Tome 19 (2022) no. 1, pp. 81-90

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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. 
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     author = {M. S. Sgibnev},
     title = {The renewal equation with unbounded inhomogeneous term},
     journal = {Sibirskie \`elektronnye matemati\v{c}eskie izvesti\^a},
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     year = {2022},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SEMR_2022_19_1_a27/}
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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/