Geodesic
Integral equations with substochastic kernels
Eurasian mathematical journal, Tome 5 (2014) no. 4, pp. 25-32.

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The non-homogeneous or homogeneous integral equation of the second kind with a substochastic kernel $W(x,t)=K(x-t)+T(x,t)$ is considered on the semi axis, where $K$ is the density of distribution of some variate, and $T\ge0$ satisfies the condition $\lambda(t)=\int^\infty_{-t}K(y)\,dy+\int^\infty_0T(x,t)\,dx1$, $\sup\lambda(t)=1$. The existence of a minimal positive solution of the non-homogeneous equation is proved. The existence of a positive solution of the homogeneous equation is also proved under some simple additional conditions. The results may be applied to the study of Random Walk on the semi axis with the reflection at the boundary. 
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A. G. Barseghyan. Integral equations with substochastic kernels. Eurasian mathematical journal, Tome 5 (2014) no. 4, pp. 25-32. http://geodesic.mathdoc.fr/item/EMJ_2014_5_4_a1/

[1] S. M. Andriyan, A. Kh. Khachatryan, “On a problem of physical kinetics”, Computational Mathematics and Mathematical Physics, 45:11 (2005), 1982–1989 | MR | Zbl

[2] L. G. Arabadzhyan, N. B. Engibaryan, “Convolution equations and nonlinear functional equations”, J. Math. Sci., 36:6 (1987), 745–791 | DOI | Zbl

[3] A. G. Barseghyan, “On a distribution of sums of identically distributed random variables”, Teor. Veroyatnost. i Primenen., 57:1 (2012), 155–158 | DOI | MR | Zbl

[4] J. Casti, R. Kalaba, Imbedding methods in applied mathematics, Series Applied Mathematics and Computation, 2, Addison-Wesley Publishing Company, Reading, Mass.–London–Amsterdam, 1973 | MR | Zbl

[5] C. Cercingnani, Theory and application of the Boltzmann equation, Elsevier, New York, 1975 | MR

[6] N. B. Engibaryan, “On the fixed points of monotonic operators in the critical case”, Izvestiya: Mathematics, 70:5 (2006), 931–947 | DOI | MR | Zbl

[7] N. R. Hansen, “The maximum of a random walk reflected at a general barrier”, The Annals of Applied Probability, 16:1 (2006), 15–29 | DOI | MR | Zbl

[8] D. V. Lindley, “The theory of queue with a single server”, Proc. Cambridge Phil. Soc., 48 (1952), 277–289 | DOI | MR

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

[10] N. Wiener, E. Hopf, “Über eine Klasse singulärer Integralgleichungen”, Sitz. Akad. Wiss. Berlin, 1931 (1931), 696–706 | Zbl