The PDF file you selected should load here if your Web browser has a PDF reader plug-in installed (for example, a recent version of Adobe Acrobat Reader).

Alternatively, you can also download the PDF file directly to your computer, from where it can be opened using a PDF reader. To download the PDF, click the Download link below.

If you would like more information about how to print, save, and work with PDFs, Highwire Press provides a helpful Frequently Asked Questions about PDFs.

Download this PDF file Fullscreen Fullscreen Off


  • Denis, Laurent; Hu, Mingshang; Peng, Shige. Function spaces and capacity related to a sublinear expectation: application to $G$-Brownian motion paths. Potential Anal. 34 (2011), no. 2, 139--161. MR2754968
  • Denis, Laurent; Martini, Claude. A theoretical framework for the pricing of contingent claims in the presence of model uncertainty. Ann. Appl. Probab. 16 (2006), no. 2, 827--852. MR2244434
  • 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
  • El Karoui, N. and Chaleyat-Maurel, M.: Un problème de réflexion et ses applications au temps local et aux équations différentielles stochastiques sur $R$, cas continu. (French) Exposés du Séminaire J. Azéma-M. Yor. Held at the Université Pierre et Marie Curie, Paris, 1976-1977, pp. 117--144. Astérisque, 52, 53, Société Mathématique de France, Paris, 1978. MR0509476
  • El Karoui, N.; Kapoudjian, C.; Pardoux, E.; Peng, S.; Quenez, M. C. Reflected solutions of backward SDE's, and related obstacle problems for PDE's. Ann. Probab. 25 (1997), no. 2, 702--737. MR1434123
  • Gao, Fuqing. Pathwise properties and homeomorphic flows for stochastic differential equations driven by $G$-Brownian motion. Stochastic Process. Appl. 119 (2009), no. 10, 3356--3382. MR2568277
  • Gégout-Petit, A.; Pardoux, E. Équations différentielles stochastiques rétrogrades réfléchies dans un convexe. (French) [Backward stochastic differential equations reflected in a convex domain] Stochastics Stochastics Rep. 57 (1996), no. 1-2, 111--128. MR1407950
  • Hildebrandt, T. H. Definitions of Stieltjes Integrals of the Riemann Type. Amer. Math. Monthly 45 (1938), no. 5, 265--278. MR1524276
  • Hu, Ying; Tang, Shanjian. Multi-dimensional BSDE with oblique reflection and optimal switching. Probab. Theory Related Fields 147 (2010), no. 1-2, 89--121. MR2594348
  • Ikeda, Nobuyuki; Watanabe, Shinzo. Stochastic differential equations and diffusion processes. North-Holland Mathematical Library, 24. North-Holland Publishing Co., Amsterdam-New York; Kodansha, Ltd., Tokyo, 1981. xiv+464 pp. ISBN: 0-444-86172-6 MR0637061
  • Lin Y. and Bai, X.: On the existence and uniqueness of solutions to stochastic differential equations driven by G-Brownian motion with integral-Lipschitz coefficients. phActa Mathematicae Applicatae Sinica, English Series, to appear. arXiv1002.1046
  • Lions, P.-L.; Sznitman, A.-S. Stochastic differential equations with reflecting boundary conditions. Comm. Pure Appl. Math. 37 (1984), no. 4, 511--537. MR0745330
  • Nutz, Marcel. Pathwise construction of stochastic integrals. Electron. Commun. Probab. 17 (2012), no. 24, 7 pp. MR2950190
  • Matoussi, A., Possamai, D. and Zhou, C.: Second order reflected backward stochastic differential equations. phAnn. Appl. Probab., to appear. arXiv1201.0746
  • Peng, Shige. $G$-expectation, $G$-Brownian motion and related stochastic calculus of Itô type. Stochastic analysis and applications, 541--567, Abel Symp., 2, Springer, Berlin, 2007. MR2397805
  • Peng, S.: Nonlinear expectations and stochastic calculus under uncertainty. arXiv1002.4546
  • Ramasubramanian, S. Reflected backward stochastic differential equations in an orthant. Proc. Indian Acad. Sci. Math. Sci. 112 (2002), no. 2, 347--360. MR1908376
  • Revuz, Daniel; Yor, Marc. Continuous martingales and Brownian motion. Third edition. Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], 293. Springer-Verlag, Berlin, 1999. xiv+602 pp. ISBN: 3-540-64325-7 MR1725357
  • Skorohod, A. V. Stochastic equations for diffusion processes with a boundary. (Russian) Teor. Verojatnost. i Primenen. 6 1961 287--298. MR0145598
  • Skorohod, A. V. Stochastic equations for diffusion processes with boundaries. II. (Russian) Teor. Verojatnost. i Primenen. 7 1962 5--25. MR0153047
  • Soner, H. M., Touzi, N. and Zhang, J.: Dual formulation of second order target problems, phAnn. Appl. Probab., to appear. arXiv1003.6050
  • Soner, H. Mete; Touzi, Nizar; Zhang, Jianfeng. Quasi-sure stochastic analysis through aggregation. Electron. J. Probab. 16 (2011), no. 67, 1844--1879. MR2842089
  • Soner, H. Mete; Touzi, Nizar; Zhang, Jianfeng. Wellposedness of second order backward SDEs. Probab. Theory Related Fields 153 (2012), no. 1-2, 149--190. MR2925572
  • 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
  • Yamada, Toshio. On the uniqueness of solutions of stochastic differential equations with reflecting barrier conditions. Séminaire de Probabilités, X (Première partie, Univ. Strasbourg, Strasbourg, année universitaire 1974/1975), pp. 240--244. Lecture Notes in Math., Vol. 511, Springer, Berlin, 1976. MR0443085

Creative Commons License
This work is licensed under a Creative Commons Attribution 3.0 License.