Geodesic
The Wiener--Hopf equation in measures with probability kernel
Sibirskie èlektronnye matematičeskie izvestiâ, Tome 16 (2019), pp. 609-617.

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

The paper deals with a generalization of the classical Wiener–Hopf equation where the functions involved are replaced by measures. A solution in explicit form is given, which coincides with the solution found by the method of successive approximations. An asymptotic property of the solution is also established.
Keywords: integral equation, measure, Wiener–Hopf equation, probability distribution, asymptotic behavior. 
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M. S. Sgibnev. The Wiener--Hopf equation in measures with probability kernel. Sibirskie èlektronnye matematičeskie izvestiâ, Tome 16 (2019), pp. 609-617. http://geodesic.mathdoc.fr/item/SEMR_2019_16_a133/

[1] V.A. Fock, “On some integral equations of mathematical physics”, Matematicheskiĭ Sbornik, 14:1–2 (1944), 3–50 | MR | Zbl

[2] M.S. Sgibnev, “Wiener-Hopf equation whose kernel is a probability distribution”, Differential equations, 53:9 (2017), 1209–1231 | DOI | MR | Zbl

[3] M.S. Sgibnev, “On the inhomogeneous conservative Wiener-Hopf equation”, Siberian Mathematical Journal, 58:6 (2017), 1090–1103 | DOI | MR | Zbl

[4] W. Feller, An Introduction to Probability Theory and its Applications, v. II, John Wiley Sons, New York–London–Sydney, 1966 | MR | Zbl

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

[6] V.I. Dmitriev, “The Wiener-Hopf equation”, Mathematical Encyclopedia, v. 1, Sovetskaya `Entsiklopediya, M., 1977, 697–698 (Russian)

[7] F.D Gakhov, Yu.I. Cherskiĭ, Equations of the convolution type, Nauka, M., 1978 (Russian) | MR

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

[9] E. Lukacs, Characteristic Functions, Second Edition, Griffin, London, 1970 | MR | Zbl

[10] M. Loève, Probability Theory, Second Edition, D. Van Nostrand Company Inc. Princeton, New Jersey–Toronto–New York–London, 1960 | MR | Zbl