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 Izv. Akad. Nauk SSSR Ser. Mat., 1981, Volume 45, Issue 3, Pages 491–508 (Mi izv2378)

On stochastic differential equations with boundary conditions in a half-plane

S. V. Anulova

Abstract: Existence theorems are proved for solutions of stochastic differential equations with boundary conditions in a Euclidean half-space. The existence of Markov processes with given characteristics in a half-space is deduced from these theorems. The case of discontinuous coefficients is included. The usual nondegeneracy condition for the normal component of diffusion near the boundary is replaced in part by the nondegeneracy of the jump component.
Bibliography: 15 titles.

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English version:
Mathematics of the USSR-Izvestiya, 1982, 18:3, 423–437

Bibliographic databases:

UDC: 519.2
MSC: Primary 60H10, 60J25; Secondary 60H05
Revised: 19.11.1980

Citation: S. V. Anulova, “On stochastic differential equations with boundary conditions in a half-plane”, Izv. Akad. Nauk SSSR Ser. Mat., 45:3 (1981), 491–508; Math. USSR-Izv., 18:3 (1982), 423–437

Citation in format AMSBIB
\Bibitem{Anu81} \by S.~V.~Anulova \paper On stochastic differential equations with boundary conditions in a~half-plane \jour Izv. Akad. Nauk SSSR Ser. Mat. \yr 1981 \vol 45 \issue 3 \pages 491--508 \mathnet{http://mi.mathnet.ru/izv2378} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=623348} \zmath{https://zbmath.org/?q=an:0489.60067|0462.60072} \transl \jour Math. USSR-Izv. \yr 1982 \vol 18 \issue 3 \pages 423--437 \crossref{https://doi.org/10.1070/IM1982v018n03ABEH001393} 

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This publication is cited in the following articles:
1. R. A. Mikulyavichyus, “On the martingale problem”, Russian Math. Surveys, 37:6 (1982), 137–150
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3. M.G. Garroni, M.A. Vivaldi, “Quasilinear, parabolic, integro-differential problems with nonlinear oblique boundary conditions”, Nonlinear Analysis: Theory, Methods & Applications, 16:12 (1991), 1089
4. Gao Ping, “The boundary harnack principle for some degenerate elliptic operators”, Communications in Partial Differential Equations, 18:12 (1993), 2001
5. J. -L. Menaldi, M. Robin, “Ergodic control of reflected diffusions with jumps”, Appl Math Optim, 35:2 (1997), 117
6. José-Luis Menaldi, Luciano Tubaro, “Green and Poisson functions with Wentzell boundary conditions”, Journal of Differential Equations, 237:1 (2007), 77
7. R. V. Shevchuk, “Inhomogeneous diffusion processes on a half-line with jumps on its boundary”, Theory Stoch. Process., 17(33):1 (2011), 119–129
8. B. I. Kopytko, R. V. Shevchuk, “On pasting together two inhomogeneous diffusion processes on a line with the general Feller-Wentzell conjugation condition”, Theory Stoch. Process., 17(33):2 (2011), 55–70
9. Adrian Zălinescu, “Stochastic variational inequalities with jumps”, Stochastic Processes and their Applications, 2013
10. A. Yu. Pilipenko, Yu. E. Prykhodko, “Limit behavior of a simple random walk with non-integrable jump from a barrier”, Theory Stoch. Process., 19(35):1 (2014), 52–61
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