One-dimensional diffusion processes in half-bounded domains with reflection and a possible jump-like exit from a moving boundary

• Autorzy: Kopytko B. , Shevchuk R.

Identyfikatory

DOI

10.17512/jamcm.2016.4.08

• Języki publikacji: EN

Abstrakty

EN

By the method of the classical potential theory, we construct the two-parameter Feller semigroup of operators associated with such a diffusion phenomenon on a half-line with a moving boundary where either a reflection or jump phenomenon occurs at a boundary point.

Słowa kluczowe

EN

diffusion process; parabolic potential; Feller-Wentzell boundary condition

PL

proces dyfuzji; potencjał paraboliczny; warunek brzegowy Feller-Wentzell

• Wydawca: Wydawnictwo Politechniki Częstochowskiej
• Czasopismo: Journal of Applied Mathematics and Computational Mechanics
• Rocznik: 2016
• Tom: Vol. 15, nr 4
• Strony: 71--82
• Opis fizyczny: Bibliogr. 10 poz.

Twórcy

autor

Kopytko B.

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

autor

Shevchuk R.

• Vasyl Stefanyk Precarpathian National University Ivano-Frankivsk, 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] Shevchuk R.V., Inhomogeneous diffusion processes on a half-line, generated by the differential operator with Feller-Wentzell boundary condition, Math. Bull. NTSH 2011, 8, 243-257 (in Ukrainian).
• [4] 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.
• [5] Portenko M.I., Diffusion Processes in Media with Membranes, Institute of Mathematics of the NAS of Ukraine, Kyiv 1995 (in Ukrainian).
• [6] Pilipenko A.Yu., On the Skorokhod mapping for equations with reflection and possible jump-like exit from a boundary, Ukrainian Math. J. 2012, 63(9), 1415-1432.
• [7] 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).
• [8] Ladyzhenskaya O.A., Solonnikov V.A., Ural’tseva N.N., Linear and Quasilinear Equations of Parabolic Type, Nauka, Moscow 1967 (in Russian).
• [9] Friedman A., Partial Differential Equations of Parabolic Type, Mir, Moscow 1968 (in Russian).
• [10] Dynkin E.B., Markov Processes, Fizmatgiz, Moscow 1963 (in Russian).

Uwagi

Opracowanie ze środków MNiSW w ramach umowy 812/P-DUN/2016 na działalność upowszechniającą naukę.