References

  1. Dynkin E.B. Markov processes. Gosudarstv. Izdat. Fiz.-Mat. Lit., Moscow, 1963. (in Russian)
  2. Feller W. The parabolic differential equations and associated semi-groups of transformations. Ann. of Math. 1952, 55, 468-519. doi: 10.2307/1969644
  3. Friedman A. Partial differential equations of parabolic type. Prentice-Hall, Englewood Cliffs, New Jersey, 1964.
  4. Holmgren E. Sur une application de l'équation de M. Volterra. Arkiv för Matematik, Astronomi och Fysik 1907, 3 (12), 1-4.
  5. 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.
  6. Kopytko B.I., Shevchuk R.V. On Feller semigroup generated by solution of nonlocal parabolic conjugation problem. Carpathian Math. Publ. 2018, 10 (2), 333-345. doi: 10.15330/cmp.10.2.333-345
  7. Ladyzhenskaya O.A., Solonnikov V.A., Ural’tseva N.N. Linear and Quasilinear Equations of Parabolic Type. Nauka, Moscow, 1967. (in Russian)
  8. 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. (in Russian)
  9. 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)
  10. Shevchuk R.V. Pasting of two one-dimensional diffusion processes. Annales Mathematicae et Informaticae 2012, 39, 225-239.
  11. Skubachevskii A.L. On Feller semigroups for multidimensional diffusion processes. Dokl. AN SSSR 1995, 341 (2), 173-176. (in Russian)
  12. 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)
  13. Wentzell A.D. On boundary conditions for multi-dimensional diffusion processes. Theory Probab. Appl. 1959, 4 (2), 164-177. doi: 10.1137/1104014