Multidimensional diffusion process with partial reflection on a fixed hyperplane and with generalized diffusion characteristics
Teoriâ slučajnyh processov, Tome 16 (2010) no. 1, pp. 73-83.

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We investigate the problem on pasting two parts of a diffusion process with variable coefficients on a hyperplane with additional conjugation condition of the Wentzel type given on it. A semigroup of operators that describe the unknown generalized diffusion process is obtained by using the method of classical potential theory.
Keywords: generalized characteristics, analytical methods.
Mots-clés : Diffusion process
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A. F. Novosyadlo. Multidimensional diffusion process with partial reflection on a fixed hyperplane and with generalized diffusion characteristics. Teoriâ slučajnyh processov, Tome 16 (2010) no. 1, pp. 73-83. http://geodesic.mathdoc.fr/item/THSP_2010_16_1_a9/

[1] A. D. Wentzel, “On boundary conditions for multidimensional diffusion process”, Probab. Theory Appl., 4 (1959), 172–185

[2] E. B. Dynkin, Markov Processes, Plenum, New York, 1969

[3] B. I. Kopytko, N. I. Portenko, “Analytical methods of pasting together of diffusion processes”, Lecture Notes in Mathematics, 1021, 1983, 320–326

[4] N. I. Portenko, Generalized Diffusion Processes, Amer. Math. Soc., Providence, RI, 1990

[5] B. I. Kopytko, “Semigroups of operators that describe a diffusion process in domain with general boundary conditions”, Dopov. NAN Ukr., 1995, no. 9, 15–18

[6] B. V. Bazalii, “On one model problem with second derivatives on geometrical variables in boundary condition for parabolic equation of the second order”, Math. Zam., 63:3 (1998), 468–473

[7] S. V. Anulova, “Diffusion processes with singular characteristics”, Intern. Symposium on Stochastic Differ. Equations (Vilnius, 1978), 7–11

[8] L. L. Zaitseva, “On stochastic continuity of generalized diffusion processes constructed as the strong solution to an SDE”, Theory of Stochastic Processes, 11 (27):12 (2005), 125–135

[9] N. Ikeda, S. Watanabe, Stochastic Differential Equations and Diffusion Processes, North-Holland, Amsterdam, 1981

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

[11] S. D. Ivasyshen, Green's Matrices of Parabolic Boundary-Value Problems, Vyshchya Shkola, Kiev, 1990 (in Russian)

[12] Ye. A. Baderko, “Solution of problem with angled derivative for parabolic equation using method of boundary integral equations”, Diff. Uravn., 25:1 (1989), 14–20

[13] C. Miranda, Partial Differential Equations of Elliptic Type, Springer, Berlin, 1970

[14] A. N. Konjenkov, “On the relation between the fundamental solution of elliptic and parabolic equations”, Diff. Uravn., 38:2 (2002), 245–256