The problem of pasting together two diffusion processes and classical potentials
Teoriâ slučajnyh processov, Tome 15 (2009) no. 2, pp. 126-139.

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The paper is a survey of some analytical methods for constructing a diffusion process in ${\mathbb R}^d$ that is a result of pasting together two diffusion processes. It is an exposition in written of a lecture that the authors delivered at one of the plenary sessions of the Conference “Stochastic analysis and random dynamics” which held in Lviv, June 14–20, 2009.
Keywords: stochastic differential equation, single-layer potentials, martingale problem.
Mots-clés : Diffusion processes
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Bohdan I.Kopytko; Mykola I. Portenko. The problem of pasting together two diffusion processes and classical potentials. Teoriâ slučajnyh processov, Tome 15 (2009) no. 2, pp. 126-139. http://geodesic.mathdoc.fr/item/THSP_2009_15_2_a8/

[1] Amer. Math. Soc., Providence, RI | MR | Zbl

[2] O. V. Aryasova, V. I. Portenko, “One example of a random change of time that transforms a generalized diffusion process into an ordinary one”, Theory Stochast. Processes, 13(29):3 (2007), 12–21 | MR | Zbl

[3] A. D. Wentzel, “On boundary conditions for multidimensional diffusion processes”, Theor. Prob. and Appl., 2:5 (1959), 172–185

[4] B. I. Kopytko, Zh. Ja. Tsapovska, “Diffusion processes with discontinuous local characteristics of the movement”, Theory Stochast. Processes, 4(20):1-2 (1998), 139–146 | MR | Zbl

[5] B. I. Kopytko, Zh. Ja. Tsapovska, “A multidimensional model of the diffusion process with a membrane whose properties are described by a general Wentzel boundary condition”, Theory Stochast. Processes, 12(28):1-2 (2006), 77–86 | MR | Zbl

[6] B. I. Kopytko, Zh. Ja. Tsapovska, “Initial boundary value problem with the conjugation condition of the Wentzel type for a parabolic equation with discontinuous coefficients”, Math. Methods and Phys.-Mech. Fields, 51:1 (2008), 7–16 (in Ukrainian) | Zbl

[7] B. I. Kopytko, A. F. Novosyadlo, “The Brownian motion process with generalized diffusion matrix and drift vector”, Theory Stochast. Processes, 14(30):2 (2008), 60–70 | MR | Zbl

[8] E. A. Baderko, “On solving the first boundary-value problem for a parabolic equation with the use of a single-layer potential”, Dokl. AN SSSR, 283:1 (1985), 11–13 (in Russian) | MR | Zbl

[9] M. R. Cherepova, On solving by the method of potentials the first boundary-value problem for a parabolic equation of the second order in a non-cylindrical domain, Dep. VINITI, no. 361–85 Dep., 1985 (in Russian)

[10] L. L. Zaitseva, “On a probabilistic approach to the construction of the generalized diffusion processes”, Theory Stochast. Processes, 6(22):1–2 (2000), 141–146 | MR

[11] B. I. Kopytko, M. I. Portenko, “One more example of a diffusion process whose local characteristics do not determine uniquely its transition probability”, Theory Stochast. Processes, 11(27):1–2 (2005), 74–80 | MR | Zbl

[12] M. I. Portenko, “On a renewal equation arisen in some problems of the theory of generalized diffusion processes”, Ukrainian Mathem. Journ., 57:9 (2005), 1302–1312 | MR | Zbl