One-dimensional model of the diffusion process with a membrane that is described by the Feller--Wentzel conjugation condition
Teoriâ slučajnyh processov, Tome 17 (2011) no. 1, pp. 61-69.

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An integral representation of the operator semigroup that corresponds to the most general nonbreaking Feller process on a line that is pasted from two diffusion processes is constructed, by using analytical methods.
Keywords: potential theory, analytical methods.
Mots-clés : Diffusion process
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P. P. Kononchuk. One-dimensional model of the diffusion process with a membrane that is described by the Feller--Wentzel conjugation condition. Teoriâ slučajnyh processov, Tome 17 (2011) no. 1, pp. 61-69. http://geodesic.mathdoc.fr/item/THSP_2011_17_1_a6/

[1] H. Langer, W. Schenk, “Knotting of one-dimensional Feller process”, Math. Nachr., 118 (1983), 151–161

[2] W. Feller, “The parabolic differential equations and the associated semigroups of transformations”, Ann. Math., 55 (1952), 468–519

[3] A. D. Wentzel, “Operator semigroups that correspond to a generalized second-order differential operator”, Doklady Akad. Nauk SSSR, 111:2 (1956), 269–272

[4] M. I. Portenko, Diffusion Processes in Media with Membranes, Institute of Mathematics of the NAS of Ukraine, Kyiv, 1995 (in Ukrainian)

[5] B. I. Kopytko, “On the pasting of two diffusion processes on a line”, Probabilistic Methods of Infinite-Dimensional Analysis, Kyiv, 1980, 84–101 (in Russian)

[6] S. I. Huran, B. I. Kopytko, “One-dimensional diffusion model with partial reflection and delay at a fixed point”, Matem. Stud., 23:1 (2005), 103–107

[7] Pavlo Kononchuk, “Pasting of two diffusion processes on a line with nonlocal boundary conditions”, Theory of Stochastic Processes, 14 (30):2 (2008), 52–59

[8] O. A. Ladyzhenskaya, V. A. Solonnikov, N. N. Ural'tseva, Linear and Quasilinear Equations of Parabolic Type, Amer. Math. Soc., Providence, RI, 1968

[9] H. L. Kulinich, “On an estimation of the trend parameter of a stochastic diffusion equation”, Theor. Prob. and Appl., 2:20 (1975), 393–397

[10] L. I. Kamynin, “On the solution of basic boundary-value problems for one-dimensional second-order parabolic equation using the method of potentials”, Sib. Math. J., 15:4 (1974), 806–834

[11] A. Friedman, Partial Differential Equations of Parabolic Type, Prentice Hall, Englewood Cliffs, NJ, 1964