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References

  • Alibert, Jean-Jacques; Bahlali, Khaled. Genericity in deterministic and stochastic differential equations. Séminaire de Probabilités, XXXV, 220--240, Lecture Notes in Math., 1755, Springer, Berlin, 2001. MR1837290
  • Bahlali, Khaled; Elouaflin, Abouo; Pardoux, Étienne. Homogenization of semilinear PDEs with discontinuous averaged coefficients. Electron. J. Probab. 14 (2009), no. 18, 477--499. MR2480550
  • Boufoussi, Brahim; Van Casteren, Jan. An approximation result for a nonlinear Neumann boundary value problem via BSDEs. Stochastic Process. Appl. 114 (2004), no. 2, 331--350. MR2101248
  • El Karoui, Nicole. Backward stochastic differential equations: a general introduction. Backward stochastic differential equations (Paris, 1995–1996), 7--26, Pitman Res. Notes Math. Ser., 364, Longman, Harlow, 1997. MR1752672
  • El Karoui, Nicole. Processus de reflexion dans $R^{n}$. (French) Séminaire de Probabilités, IX (Seconde Partie, Univ. Strasbourg, Strasbourg, années universitaires 1973/1974 et 1974/1975), pp. 534--554. Lecture Notes in Math., Vol. 465, Springer, Berlin, 1975. MR0423554
  • Jakubowski, Adam. A non-Skorohod topology on the Skorohod space. Electron. J. Probab. 2 (1997), no. 4, 21 pp. (electronic). MR1475862
  • Karatzas, Ioannis; Shreve, Steven E. Brownian motion and stochastic calculus. Graduate Texts in Mathematics, 113. Springer-Verlag, New York, 1988. xxiv+470 pp. ISBN: 0-387-96535-1 MR0917065
  • Łaukajtys, Weronika; Słomiński, Leszek. Penalization methods for reflecting stochastic differential equations with jumps. Stoch. Stoch. Rep. 75 (2003), no. 5, 275--293. MR2017780
  • Łaukajtys, Weronika; Słomiński, Leszek. Penalization methods for the Skorokhod problem and reflecting SDEs with jumps. Bernoulli 19 (2013), no. 5A, 1750-1775.
  • Lejay, Antoine. BSDE driven by Dirichlet process and semi-linear parabolic PDE. Application to homogenization. Stochastic Process. Appl. 97 (2002), no. 1, 1--39. MR1870718
  • Lions, Pierre-Louis; Menaldi, José-Luis; Sznitman, Alain-Sol. Construction de processus de diffusion réfléchis par pénalisation du domaine. (French) C. R. Acad. Sci. Paris Sér. I Math. 292 (1981), no. 11, 559--562. MR0614669
  • Lions, Pierre-Louis; Sznitman, Alain-Sol. Stochastic differential equations with reflecting boundary conditions. Comm. Pure Appl. Math. 37 (1984), no. 4, 511--537. MR0745330
  • Maticiuc, Lucian; Răşcanu, Aurel. Viability of moving sets for a nonlinear Neumann problem. Nonlinear Anal. 66 (2007), no. 7, 1587--1599. MR2301340
  • Menaldi, José-Luis. Stochastic variational inequality for reflected diffusion. Indiana Univ. Math. J. 32 (1983), no. 5, 733--744. MR0711864
  • Pardoux, Étienne. BSDEs, weak convergence and homogenization of semilinear PDEs. Nonlinear analysis, differential equations and control (Montreal, QC, 1998), 503--549, NATO Sci. Ser. C Math. Phys. Sci., 528, Kluwer Acad. Publ., Dordrecht, 1999. MR1695013
  • Pardoux, Étienne; Zhang, Shuguang. Generalized BSDEs and nonlinear Neumann boundary value problems. Probab. Theory Related Fields 110 (1998), no. 4, 535--558. MR1626963
  • Pardoux, Étienne; Răşcanu, Aurel. Stochastic differential equations, Backward SDEs, Partial differential equations. Stochastic Modelling and Applied Probability, Springer, in press, 2014.
  • Rozkosz, Andrzej; Słomiński, Leszek. On stability and existence of solutions of SDEs with reflection at the boundary. Stochastic Process. Appl. 68 (1997), no. 2, 285--302. MR1454837
  • Skorokhod, A. V. Studies in the theory of random processes. Translated from the Russian by Scripta Technica, Inc. Addison-Wesley Publishing Co., Inc., Reading, Mass., 1965 viii+199 pp. MR0185620
  • Stricker, Christophe. Lois de semimartingales et critères de compacité. (French) [Laws of semimartingales and compactness criteria] Séminaire de probabilités, XIX, 1983/84, 209--217, Lecture Notes in Math., 1123, Springer, Berlin, 1985. MR0889478
  • Stroock, Daniel W.; Varadhan, S. R. S. Diffusion processes with boundary conditions. Comm. Pure Appl. Math. 24 1971 147--225. MR0277037
  • Tanaka, Hiroshi. Stochastic differential equations with reflecting boundary condition in convex regions. Hiroshima Math. J. 9 (1979), no. 1, 163--177. MR0529332
  • Zălinescu, Adrian. Weak solutions and optimal control for multivalued stochastic differential equations. NoDEA Nonlinear Differential Equations Appl. 15 (2008), no. 4-5, 511--533. MR2465976


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