Geodesic
On the representation of the Goursat boundary problem solution for the first order partial derivatives stochastic hyperbolic equations
The Bulletin of Irkutsk State University. Series Mathematics, Tome 45 (2023), pp. 145-151

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We study the standard canonical form of a stochastic analog of a system of linear partial differential equations of first order hyperbolic type with Goursat boundary conditions. The stochastic analogue of the Riemann matrix in block form is introduced, an integral representation of the solution of the boundary value problem under consideration is obtained in an explicit integral form in terms of boundary conditions.
Keywords: linear inhomogeneous stochastic Goursat system, stochastic boundary value problem, Wiener process, explicit representation of the solution. 
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     author = {K. B. Mansimov and R. O. Mastaliyev},
     title = {On the representation of the {Goursat} boundary problem solution for the first order partial derivatives stochastic hyperbolic equations},
     journal = {The Bulletin of Irkutsk State University. Series Mathematics},
     pages = {145--151},
     publisher = {mathdoc},
     volume = {45},
     year = {2023},
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     url = {http://geodesic.mathdoc.fr/item/IIGUM_2023_45_a9/}
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K. B. Mansimov; R. O. Mastaliyev. On the representation of the Goursat boundary problem solution for the first order partial derivatives stochastic hyperbolic equations. The Bulletin of Irkutsk State University. Series Mathematics, Tome 45 (2023), pp. 145-151. http://geodesic.mathdoc.fr/item/IIGUM_2023_45_a9/