D. Applebaum, Lévy Processes and Stochastic Calculus, 2009.

G. Barles, Nonlinear Neumann Boundary Conditions for Quasilinear Degenerate Elliptic Equations and Applications, Journal of Differential Equations, vol.154, issue.1, pp.191-224, 1999.
DOI : 10.1006/jdeq.1998.3568

G. Barles, R. Buckdahn, and E. Pardoux, Backward stochastic differential equations and integral-partial differential equations, Stochastics An International Journal of Probability and Stochastic Processes, vol.60, issue.1, pp.57-83, 1997.
DOI : 10.1080/17442509708834099

G. Barles, E. Chasseigne, C. Georgelin, and E. , Jakobsen On Neumann type problems for nonlocal equations set in a half space, 2011.

G. Barles and E. , On the Dirichlet problem for second-order elliptic integro-differential equations, Indiana University Mathematics Journal, vol.57, issue.1, pp.213-146, 2008.
DOI : 10.1512/iumj.2008.57.3315
URL : https://hal.archives-ouvertes.fr/hal-00150151

G. Barles and C. , Second-order elliptic integro-differential equations: viscosity solutions' theory revisited, Annales de l'Institut Henri Poincare (C) Non Linear Analysis, vol.25, issue.3, pp.567-585, 2008.
DOI : 10.1016/j.anihpc.2007.02.007
URL : https://hal.archives-ouvertes.fr/hal-00130169

G. Barles and P. Lions, Remarques sur lesprobì emes de réflexion oblique, pp.69-74, 1995.

G. Barles, S. Mirrahimi, B. Perthame, and P. E. , Souganidis : Singular Hamilton-Jacobi equation for the tail problem

L. Caffarelli and L. Silvestre, An Extension Problem Related to the Fractional Laplacian, Communications in Partial Differential Equations, vol.32, issue.8, pp.1245-1260, 2007.
DOI : 10.1080/00036818308839425

R. Cont and P. Tankov, Financial modelling with jump processes, 2004.
DOI : 10.1201/9780203485217
URL : https://hal.archives-ouvertes.fr/hal-00002693

M. Crandall, H. Ishii, and P. Lions, user's guide to viscosity solutions\\ of second order\\ partial differential equations, Bulletin of the American Mathematical Society, vol.27, issue.1, pp.1-67, 1992.
DOI : 10.1090/S0273-0979-1992-00266-5

M. G. Garroni and J. L. Menaldi, Second order elliptic integro-differential problems, 2002.

I. I. Gihman and A. V. Skorohod, Stochastic Differential Equations, 1972.
DOI : 10.1007/978-3-642-88264-7

Q. Y. Guan, Integration by Parts Formula for Regional Fractional Laplacian, Communications in Mathematical Physics, vol.71, issue.11???12, pp.289-329, 2006.
DOI : 10.1007/s00220-006-0054-9

Q. Y. Guan and Z. M. Ma, Reflected symmetric ?-stable processes and regional fractional Laplacian. Prob. Theory Relat, pp.649-694, 2006.

Q. Y. Guan and Z. M. Ma, BOUNDARY PROBLEMS FOR FRACTIONAL LAPLACIANS, Stochastics and Dynamics, vol.05, issue.03, pp.385-424, 2005.
DOI : 10.1142/S021949370500150X

P. Hsu, On excursions of reflecting Brownian motion, Transactions of the American Mathematical Society, vol.296, issue.1, 1986.
DOI : 10.1090/S0002-9947-1986-0837810-X

E. R. Jakobsen and K. H. Karlsen, A Maximum principle for semicontinuous functions applicable to integro-partial differential equations Nonlinear Differential Equations and Applications, 2006.

P. L. Lions and A. S. Sznitman, Stochastic differential equations with reflecting boundary conditions, Communications on Pure and Applied Mathematics, vol.11, issue.4, pp.511-537, 1984.
DOI : 10.1002/cpa.3160370408

P. Lions, J. L. Menaldi, and A. , Sznitman Construction de processus de diffusion réfléchis par pénalisation du domaine. CRAS Paris I-292, pp.559-562, 1981.

R. R. Mazumdar-1 and E. M. Guillemin, Forward equations for reflected diffusions with jumps, Applied Mathematics & Optimization, vol.31, issue.4, pp.81-102, 1996.
DOI : 10.1007/BF01187963

J. L. Menaldi and M. , Robin Reflected Diffusion Processes with Jumps. The Annals of Probability, pp.319-341, 1985.
DOI : 10.1214/aop/1176992994

H. Pham, Optimal stopping of controlled jump diffusion processes: a viscosity solution approach, J. Math. Systems Estim. Control, vol.8, issue.1, 1998.