On the existence of a solution of a homogeneous system of generalized Wiener--Hopf equations
Izvestiya. Mathematics , Tome 74 (2010) no. 3, pp. 595-606.

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We prove the existence of a non-decreasing solution of a homogeneous system of generalized Wiener–Hopf equations and establish asymptotic properties of this solution.
Keywords: system of integral equations, homogeneous system of Wiener–Hopf equations, matrix of measures, matrix reconstruction function, asymptotic behaviour.
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M. S. Sgibnev. On the existence of a solution of a homogeneous system of generalized Wiener--Hopf equations. Izvestiya. Mathematics , Tome 74 (2010) no. 3, pp. 595-606. http://geodesic.mathdoc.fr/item/IM2_2010_74_3_a6/

[1] F. Spitzer, “The Wiener–Hopf equation whose kernel is a probability density”, Duke Math. J., 24:3 (1957), 327–343 | DOI | MR | Zbl

[2] F. Spitzer, “The Wiener–Hopf equation whose kernel is a probability density. II”, Duke Math. J., 27:3 (1960), 363–372 | DOI | MR | Zbl

[3] N. B. Engibaryan, “Conservative systems of integral convolution equations on the half-line and the entire line”, Sb. Math., 193:6 (2002), 847–867 | DOI | MR | Zbl

[4] M. S. Sgibnev, “Homogeneous conservative Wiener–Hopf equation”, Sb. Math., 198:9 (2007), 1341–1350 | DOI | MR | Zbl

[5] V. Feller, Vvedenie v teoriyu veroyatnostei i ee prilozheniya, v. 2, Mir, M., 1967 ; W. Feller, An introduction to probability theory and its applications, v. II, Wiley, New York–London–Sydney, 1966 | MR | Zbl | MR | Zbl

[6] S. Asmussen, “Aspects of matrix Wiener–Hopf factorisation in applied probability”, Math. Sci., 14:2 (1989), 101–116 | MR | Zbl

[7] R. Khorn, Ch. Dzhonson, Matrichnyi analiz, Mir, M., 1989 ; R. A. Horn, Ch. R. Johnson, Matrix analysis, Cambridge Univ. Press, Cambridge, 1985 | MR | Zbl | MR | Zbl

[8] M. Newbould, “A classification of a random walk defined on a finite Markov chain”, Z. Wahrscheinlichkeitstheorie und Verw. Gebiete, 26:2 (1973), 95–104 | DOI | MR | Zbl

[9] È. L. Presman, “Factorization methods and boundary problems for sums of random variables given on Markov chains”, Math. USSR-Izv., 3:4 (1969), 815–852 | DOI | MR | Zbl | Zbl

[10] M. S. Sgibnev, “The matrix analogue of the Blackwell renewal theorem on the real line”, Sb. Math., 197:3 (2006), 369–386 | DOI | MR | Zbl

[11] P. Lankaster, Teoriya matrits, Nauka, M., 1982 ; P. Lancaster, Theory of matrices, Academic Press, New York–London, 1969 | MR | Zbl | MR | Zbl

[12] P. Khalmosh, Teoriya mery, IL, M., 1953 ; P. R. Halmos, Measure theory, Nostrand, New York; Macmillan, London, 1950 | MR | MR | Zbl

[13] E. Lukach, Kharakteristicheskie funktsii, Nauka, M., 1979 ; E. Lukacs, Characteristic functions, Hafner Publ., New York, 1970 | MR | Zbl | MR | Zbl

[14] K. S. Crump, “On systems of renewal equations”, J. Math. Anal. Appl., 30:2 (1970), 425–434 | DOI | MR | Zbl