References

  1. Anulova S.V. Diffusion processes: discontinuous coefficients, degenerate diffusion, randomized drift. Dokl. Akad. Nauk 1981, 260 (5), 1036–1040. (in Russian)
  2. Dynkin E.B. Markov processes. Gosudarstv. Izdat. Fiz.-Mat. Lit., Moscow, 1963. (in Russian)
  3. Engelbert H.J., Schmidt W. Strong Markov continuous local martingales and solutions of one-dimensional stochastic differential equations. III. Math. Nachr. 1991, 151 (1), 149–197. doi:10.1002/mana.19911510111
  4. Feller W. The parabolic differential equations and the associated semi-groups of transformations. Ann. of Math.(2) 1952, 55 (3), 468–519. doi:10.2307/1969644
  5. Friedman A. Partial differential equations of parabolic type. Prentice-Hall, Englewood Cliffs, New Jersey, 1964.
  6. Ikeda N., Watanabe S. Stochastic differential equations and diffusion processes. North-Holland Mathematical Library 24, North-Holland Publishing Co., Amsterdam-New York, Kodansha, Ltd., Tokyo, 1981.
  7. Kamynin L.I. A boundary value problem in the theory of heat conduction with a nonclassical boundary condition. Zh. Vychisl. Mat. Mat. Fiz. 1964, 4 (6), 1006–1024.
  8. Kamynin L.I., Khimchenko B.N On applications of the maximum principle to parabolic equations of second order. Dokl. Akad. Nauk 1972, 204 (3), 529–532. (in Russian)
  9. Kopytko B.I., Shevchuk R.V. On pasting together two inhomogeneous diffusion processes on a line with the general Feller-Wentzell conjugation condition. Theory Stoch. Process. 2011, 17 (2), 55–70.
  10. 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.
  11. Kopytko B.I., Shevchuk R.V. One-dimensional diffusion processes with moving membrane: partial reflection in combination with jump-like exit of process from membrane. Electron. J. Probab. 2020, 25 (41), 1–21. doi:10.1214/20-EJP443
  12. Ladyzhenskaya O.A., Solonnikov V.A., Ural’tseva N.N. Linear and Quasilinear Equations of Parabolic Type. Nauka, Moscow, 1967. (in Russian)
  13. Langer H., Schenk W. Knotting of one-dimensional Feller processes. Math. Nachr. 1983, 113 (1), 151–161. doi:10.1002/mana.19831130115
  14. 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. doi:10.1007/s11253-012-0588-2
  15. Pogorzelski W. Integral equations and their applications. Tom IV. PWN-Polish Scientific Publishers, Warsaw, 1970. (in Polish)
  16. Portenko M.I. Diffusion Processes in Media with Membranes. Proceedings of the Institute of Mathematics of the National Academy of Sciences of the Ukraine, Kyiv, 1995. (in Ukrainian)
  17. Skorokhod A.V. Stochastic equations for diffusion processes in a bounded region. Theory Probab. Appl. 1961, 6 (3), 264–274. doi:10.1137/1106035
  18. Skubachevskii A.L. Nonlocal elliptic problems and multidimensional diffusion processes. Russ. J. Math. Phys. 1995, 3 (3), 327–360.
  19. Walsh J.B. A diffusion with a discontinuous local time. Astérisque 1978, 52–53, 37–45.
  20. Wentzell A.D. Semigroups of Operators Corresponding to a Generalized Differential Operatorof Second Order. Dokl. Akad. Nauk 1956, 111 (2), 269–272. (in Russian)
  21. Venttsel A.D. On boundary conditions for multi-dimensional diffusion processes. Theory Probab. Appl. 1959, 4 (2), 164–177. doi:10.1137/1104014