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.
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\Bibitem{Anu81}
\by S.~V.~Anulova
\paper On stochastic differential equations with boundary conditions in a~half-plane
\jour Math. USSR-Izv.
\yr 1982
\vol 18
\issue 3
\pages 423--437
\mathnet{http://mi.mathnet.ru/eng/im2378}
\crossref{https://doi.org/10.1070/IM1982v018n03ABEH001393}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=623348}
\zmath{https://zbmath.org/?q=an:0489.60067|0462.60072}
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https://doi.org/10.1070/IM1982v018n03ABEH001393
https://www.mathnet.ru/eng/im/v45/i3/p491
This publication is cited in the following 13 articles:
Andrey Pilipenko, Andrey Sarantsev, “Boundary approximation for sticky jump-reflected processes on the half-line”, Electron. J. Probab., 29:none (2024)
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
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
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
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