Geodesic
The Wiener–Hopf equation with probability kernel of oscillating type
Sibirskie èlektronnye matematičeskie izvestiâ, Tome 17 (2020), pp. 1288-1298

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We prove the existence of a solution to the inhomogeneous Wiener–Hopf equation whose kernel is a nonarithmetic probability distribution generating an oscillating random walk. Asymptotic properties of the solution are established depending on the properties of the inhomogeneous term of the equation.
Keywords: integral equation, inhomogeneous equation, Wiener-Hopf equation, asymptotic behavior, nonarithmetic distribution, oscillating type. 
@article{SEMR_2020_17_a137,
     author = {M. S. Sgibnev},
     title = {The {Wiener{\textendash}Hopf} equation with probability kernel of oscillating type},
     journal = {Sibirskie \`elektronnye matemati\v{c}eskie izvesti\^a},
     pages = {1288--1298},
     publisher = {mathdoc},
     volume = {17},
     year = {2020},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SEMR_2020_17_a137/}
}
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M. S. Sgibnev. The Wiener–Hopf equation with probability kernel of oscillating type. Sibirskie èlektronnye matematičeskie izvestiâ, Tome 17 (2020), pp. 1288-1298. http://geodesic.mathdoc.fr/item/SEMR_2020_17_a137/