Geodesic
The discrete Wiener--Hopf equation with submultiplicative asymptotics of the solution
Sibirskie èlektronnye matematičeskie izvestiâ, Tome 16 (2019), pp. 1600-1611.

Voir la notice de l'article provenant de la source Math-Net.Ru

The discrete Wiener–Hopf equation is considered whose kernel is an arithmetic probability distribution with positive mean. The nonhomogeneous term behaves like a nondecreasing submultiplicative sequence. Asymptotic properties of the solution are established depending on the asymptotics of the submultiplicative sequence.
Keywords: discrete Wiener–Hopf equation, nonhomogeneous equation, arithmetic probability distribution, positive mean, submultiplicative sequence, regularly varying function, asymptotic behavior. 
@article{SEMR_2019_16_a142,
     author = {M. S. Sgibnev},
     title = {The discrete {Wiener--Hopf} equation with submultiplicative asymptotics of the solution},
     journal = {Sibirskie \`elektronnye matemati\v{c}eskie izvesti\^a},
     pages = {1600--1611},
     publisher = {mathdoc},
     volume = {16},
     year = {2019},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SEMR_2019_16_a142/}
}
TY  - JOUR
AU  - M. S. Sgibnev
TI  - The discrete Wiener--Hopf equation with submultiplicative asymptotics of the solution
JO  - Sibirskie èlektronnye matematičeskie izvestiâ
PY  - 2019
SP  - 1600
EP  - 1611
VL  - 16
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/SEMR_2019_16_a142/
LA  - ru
ID  - SEMR_2019_16_a142
ER  - 
%0 Journal Article
%A M. S. Sgibnev
%T The discrete Wiener--Hopf equation with submultiplicative asymptotics of the solution
%J Sibirskie èlektronnye matematičeskie izvestiâ
%D 2019
%P 1600-1611
%V 16
%I mathdoc
%U http://geodesic.mathdoc.fr/item/SEMR_2019_16_a142/
%G ru
%F SEMR_2019_16_a142
M. S. Sgibnev. The discrete Wiener--Hopf equation with submultiplicative asymptotics of the solution. Sibirskie èlektronnye matematičeskie izvestiâ, Tome 16 (2019), pp. 1600-1611. http://geodesic.mathdoc.fr/item/SEMR_2019_16_a142/

[1] M.G. Krein, “Integral equations on the half-line with kernel depending on the difference of the arguments”, Uspekhi Mat. Nauk, 13:5 (1958), 3–120 (In Russian) | MR

[2] W. Feller, An Introduction to Probability Theory and Its Applications, v. 2, John Wiley and Sons, Inc., New York etc., 1966 | MR | Zbl

[3] J. Neveu, Bases Mathématiques du Calcul des Probabilités, Masson et Cie, Paris, 1964 | MR

[4] A.N. Kolmogorov, S.V. Fomin, Elements of the Theory of Functions and Functional Analysis, Dover Publications, Mineola, 1999 | MR

[5] M.S. Sgibnev, “The discrete Wiener-Hopf equation with probability kernel of oscillating type”, Siberian Mathematical Journal, 60:3 (2019), 516–525 | DOI | MR | Zbl

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

[7] M.S. Sgibnev, “On the homogeneous conservative Wiener-Hopf equation”, Sbornik: Mathematics, 198:9 (2007), 1341–1350 | DOI | MR | Zbl

[8] W. Feller, An Introduction to Probability Theory and its Applications, v. 1, Second Edition, John Wiley and Sons, Inc., New York; Chapman and Hall, Limited, London, 1957 | MR | Zbl

[9] I.M. Gelfand, D.A. Raikov, G.E. Shilov, Commutative Normed Rings, Chelsea, New York, 1964 | MR

[10] M.S. Sgibnev, “Semimultiplicative moments of factors in Wiener-Hopf matrix factorization”, Sbornik: Mathematics, 199:2 (2008), 277–290 | DOI | MR | Zbl

[11] G.M. Fichtenholz, A Course of Differential and Integral Calculus, v. 1, Sixth Edition, Nauka (Fizmatlit), M., 1966 (In Russian) | MR

[12] E. Seneta, Regularly Varying Functions, Springer-Verlag, Berlin–Heidelberg–New York, 1976 | MR | Zbl

[13] M.S. Sgibnev, “Submultiplicative moments of the supremum of a random walk with negative drift”, Statist. Probab. Lett., 32 (1997), 377–383 | DOI | MR | Zbl