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.
\Bibitem{Anu78}
\by S.~V.~Anulova
\paper On processes with L\'evy generating operator in a~half-space
\jour Math. USSR-Izv.
\yr 1979
\vol 13
\issue 1
\pages 9--51
\mathnet{http://mi.mathnet.ru/eng/im1788}
\crossref{https://doi.org/10.1070/IM1979v013n01ABEH002009}
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This publication is cited in the following 12 articles:
Adrian Zălinescu, “Stochastic variational inequalities with jumps”, Stochastic Processes and their Applications, 2013
R. V. Shevchuk, “Inhomogeneous diffusion processes on a half-line with jumps on its boundary”, Theory Stoch. Process., 17(33):1 (2011), 119–129
José-Luis Menaldi, Luciano Tubaro, “Green and Poisson functions with Wentzell boundary conditions”, Journal of Differential Equations, 237:1 (2007), 77
J. -L. Menaldi, M. Robin, “Ergodic control of reflected diffusions with jumps”, Appl Math Optim, 35:2 (1997), 117
Gao Ping, “The boundary harnack principle for some degenerate elliptic operators”, Communications in Partial Differential Equations, 18:12 (1993), 2001
Maria Giovanna Garroni, Jose Luis Menaldi, “Green's function and invariant density for an integro-differential operator of second order”, Annali di Matematica, 154:1 (1989), 147
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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
José Luis Menaldi, Maurice Robin, Lecture Notes in Control and Information Sciences, 69, Stochastic Differential Systems Filtering and Control, 1984, 309
J. Menaldi, M. Robin, “On singular stochastic control problems for diffusion with jumps”, IEEE Trans. Automat. Contr., 29:11 (1984), 991
R. A. Mikulyavichyus, “On the martingale problem”, Russian Math. Surveys, 37:6 (1982), 137–150
S. V. Anulova, “On stochastic differential equations with boundary conditions in a half-plane”, Math. USSR-Izv., 18:3 (1982), 423–437
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