This article is cited in 13 papers

On processes with Lévy generating operator in a half-space

S. V. Anulova


Abstract: 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.

UDC: 519.2

MSC: Primary 60H10, 60J25; Secondary 60H05

Received: 24.06.1977

 English version: Mathematics of the USSR-Izvestiya, 1979, 13:1, 9–51

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