This article is cited in 9 scientific papers (total in 9 papers)
On processes with Lévy generating operator in a half-space
S. V. Anulova
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.
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Mathematics of the USSR-Izvestiya, 1979, 13:1, 9–51
MSC: Primary 60H10, 60J25; Secondary 60H05
S. V. Anulova, “On processes with Lévy generating operator in a half-space”, Izv. Akad. Nauk SSSR Ser. Mat., 42:4 (1978), 708–750; Math. USSR-Izv., 13:1 (1979), 9–51
Citation in format AMSBIB
\paper On processes with L\'evy generating operator in a~half-space
\jour Izv. Akad. Nauk SSSR Ser. Mat.
\jour Math. USSR-Izv.
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N. V. Krylov, “On estimates of the maximum of a solution of a parabolic equation and estimates of the distribution of a semimartingale”, Math. USSR-Sb., 58:1 (1987), 207–221
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