On processes with Lévy generating operator in a half-space

The author considers a stochastic differential equation in a half-space with boundary conditions of Ventcel'. Under mild regularity conditions imposed on the coefficients the existence of a solution is proved, and the Markov property thereof is studied. From the results the existence of a Markov process in a half-space, with corresponding generating operator and boundary conditions, is deduced. An ancillary estimate of the distribution density of a stochastic integral, which is of independent interest, is also proved.
Bibliography: 20 titles.