One-dimensional diffusions in bounded domains with a possible jump-like exit from a sticky boundary

• Autorzy: Kopytko B. , Shevchuk R.
• Języki publikacji: EN

Abstrakty

EN

Using analytical methods we obtain the integral representation of a two-parameter Feller semigroup on a closed interval [r1, r2] corresponding to such a diffusion phenomenon that sticking, partial reflection, absorption and jump phenomena occur at the endpoints r1, r2 and at some interior point r ∈ (r1,r2).

Słowa kluczowe

EN

diffusion process; parabolic potential; conjugation problem

PL

proces dyfuzji; potencjał paraboliczny

• Wydawca: Wydawnictwo Politechniki Częstochowskiej
• Czasopismo: Journal of Applied Mathematics and Computational Mechanics
• Rocznik: 2014
• Tom: Vol. 13, nr 3
• Strony: 101--114
• Opis fizyczny: Bibliogr. 15 poz.

Twórcy

autor

Kopytko B.

• Institute of Mathematics, Czestochowa University of Technology, Częstochowa, Poland

autor

Shevchuk R.

• Ivan Franko National University of Lviv, Lviv, Ukraine

Bibliografia

• [1] Feller W., The parabolic differential equations and associated semi-groups of transformations, Ann. Math. 1952, 55, 468-518.
• [2] Wentzell A.D., Semigroups of operators that correspond to a generalized differential operator of second order, Dokl. AN SSSR 1956, 111, 2, 269-272 (in Russian).
• [3] Langer H., Schenk W., Knotting of one-dimensional Feller process, Math. Nachr. 1983, 113, 151-161.
• [4] Kopytko B.I., Sewing two nonhomogeneous diffusion processes on a straight line, Ukrainian Math. Journal 1983, 35, 2, 135-141.
• [5] Portenko M.I., Diffusion Processes in Media with Membranes, Institute of Mathematics of the NAS of Ukraine, Kyiv 1995 (in Ukrainian).
• [6] Kopytko B.I., Shevchuk R.V., On pasting together two inhomogeneous diffusion processes on a line with the general Feller-Wentzell conjugation condition, Theory of Stochastic Processes 2011, 17(33), 2, 55-70.
• [7] Kopytko B.I., Shevchuk R.V., Diffusions in one-dimensional bounded domains with reflection, absorption and jumps at the boundary and at some interior point, Journal of Applied Mathematics and Computational Mechanics 2013, 12(1), 55-68.
• [8] Kopytko B.I., Shevchuk R.V., One-dimensional diffusion processes in bounded domains with boundary conditions and conjugation condition of Feller-Wentzell, Bukovinian Math. Journal 2013, 1, 1-2, 77-85.
• [9] Feller W., Diffusion processes in one dimension, Trans. Amer. Math. Soc. 1954, 77, 1-31.
• [10] Taira K., Boundary Value Problems and Markov Processes, Lecture Notes in Mathematics, 1499, Springer-Verlag, Berlin-Heidelberg 2009.
• [11] Anulova S.V., On stochastic differential equations with boundary conditions in a half-plane, Izv. AN SSSR Ser. Mat. 1981, 45, 3, 491-508 (in Russian).
• [12] Pilipenko A.Yu., On the Skorokhod mapping for equations with reflection and possible jumplike exit from a boundary, Ukrainian Math. J. 2012, 63, 9, 1415-1432.
• [13] Ladyzhenskaya O.A., Solonnikov V.A., Ural’tseva N.N., Linear and Quasilinear Equations of Parabolic Type, Nauka, Moscow 1967 (in Russian).
• [14] Friedman A., Partial Differential Equations of Parabolic Type, Mir, Moscow 1968 (in Russian).
• [15] Dynkin E.B., Markov Processes, Fizmatgiz, Moscow 1963 (in Russian).