N. Alibaud and C. Imbert, A non-local perturbation of first order Hamilton-Jacobi equations, 2007.

O. Alvarez and A. Tourin, Viscosity solutions of nonlinear integro-differential equations, Annales de l'Institut Henri Poincare (C) Non Linear Analysis, vol.13, issue.3, pp.293-317, 1996.
DOI : 10.1016/S0294-1449(16)30106-8

M. Arisawa, A new definition of viscosity solutions for a class of second-order degenerate elliptic integro-differential equations, Annales de l'Institut Henri Poincare (C) Non Linear Analysis, vol.23, issue.5, pp.695-711, 2006.
DOI : 10.1016/j.anihpc.2005.09.002

M. Arisawa, Corrigendum for the comparison theorems in: ???A new definition of viscosity solutions for a class of second-order degenerate elliptic integro-differential equations??? [Ann. I. H. Poincar?? ??? AN 23 (5) (2006) 695???711], Annales de l'Institut Henri Poincare (C) Non Linear Analysis, vol.24, issue.1, pp.167-169, 2006.
DOI : 10.1016/j.anihpc.2006.10.001

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

I. Bensaoud and A. Sayah, Stability results for Hamilton-Jacobi equations with integro-differential terms and discontinuous Hamiltonians, Archiv der Mathematik, vol.79, issue.5, pp.392-395, 2002.
DOI : 10.1007/PL00012462

J. Bertoin, Lévy processes, volume 121 of Cambridge Tracts in Mathematics, 1996.

M. G. Crandall and H. Ishii, The maximum principle for semicontinuous functions, Differential Integral Equations, vol.3, issue.6, pp.1001-1014, 1990.

M. G. 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, CRC Research Notes in Mathematics. Chapman & Hall/CRC, vol.430, 2002.

C. Imbert, A non-local regularization of first order Hamilton???Jacobi equations, Journal of Differential Equations, vol.211, issue.1, pp.218-246, 2005.
DOI : 10.1016/j.jde.2004.06.001
URL : https://hal.archives-ouvertes.fr/hal-00176542

C. Imbert, R. Monneau, and E. Rouy, /??)-Periodic Hamiltonians Part II: Application to Dislocations Dynamics, Communications in Partial Differential Equations, vol.20, issue.3
DOI : 10.1209/epl/i2003-10175-2

H. Ishii, On uniqueness and existence of viscosity solutions of fully nonlinear second-order elliptic PDE's, Communications on Pure and Applied Mathematics, vol.56, issue.1, pp.15-45, 1989.
DOI : 10.1002/cpa.3160420103

E. R. Jakobsen and K. H. Karlsen, A ???maximum principle for semicontinuous functions??? applicable to integro-partial differential equations, Nonlinear Differential Equations and Applications NoDEA, vol.13, issue.2, pp.137-165, 2006.
DOI : 10.1007/s00030-005-0031-6

R. Jensen, The maximum principle for viscosity solutions of fully nonlinear second order partial differential equations, Archive for Rational Mechanics and Analysis, vol.74, issue.1, pp.1-27, 1988.
DOI : 10.1007/BF00281780

B. Øksendal and A. Sulem, Applied stochastic control of jump diffusions, 2005.
DOI : 10.1007/978-3-540-69826-5

H. Pham, Optimal stopping of controlled jump diffusion processes: a viscosity solution approach, J. Math. Systems Estim. Control, vol.8, issue.1, p.27, 1998.

]. A. Sayah, ´ Equations d'Hamilton-Jacobi du premier ordre avec termes intégro-différentiels. I. Unicité des solutions de viscosité. II. Existence de solutions de viscosité, Comm. Partial Differential Equations, vol.16, pp.6-71057, 1991.

L. Silvestre, Holder estimates for solutions of integro differential equations like the fractional laplace, Indiana University Mathematics Journal, vol.55, issue.3, pp.1155-1174, 2006.
DOI : 10.1512/iumj.2006.55.2706

H. M. Soner, Optimal Control with State-Space Constraint I, SIAM Journal on Control and Optimization, vol.24, issue.3, pp.1110-1122, 1986.
DOI : 10.1137/0324032

W. A. Woyczy´nskiwoyczy´nski, Lévy processes in the physical sciences, Lévy processes, pp.241-266, 2001.