Homogenization of a Class of Integro-Differential Equations with Lévy Operators

References

• Alvarez , O. , Tourin , A. ( 1996 ). Viscosity solutions of nonlinear integro-differential equations . Ann. Inst. H. Poincaré, Anal. Non Linéaire 13 : 293 – 317 .
   Web of Science ®Google Scholar
• Arisawa , M. ( 2006 ). A new definition of viscosity solution for a class of second-order degenerate elliptic integro-differential equations . Inst. H. Poincaré, Anal. Non Linéare 23 : 695 – 711 .
   Google Scholar
• Arisawa , M. ( 2006 ). Corrigendum for “A new definition of viscosity solution for a class of second-order degenerate elliptic integro-differential equations” . Inst. H. Poincaré, Anal. Non Linéare 24 : 167 – 169 .
   Google Scholar
• Arisawa , M. ( 2007 ). A localization of the Lévy operators arising in mathematical finances . In: Ogawa , S. , Akahori , J. , Watanabe , S. , eds. Proceedings of the 6th RITS Symposium on Stochastic Processes and Applications to Mathematical Finance . Hackensack , NJ : World Scientific , pp. 23 – 52 .
   Google Scholar
• Arisawa , M. ( 2008 ). A remark on the definitions of viscosity solutions for the integro-differential equations with Lévy operators . J. Mathématiques Pures Appl. 89 : 567 – 574 .
   Google Scholar
• Arisawa , M. , Lions , P.-L . ( 1998 ). On ergodic stochastic control . Comm. Partial Differential Equations 23 : 2187 – 2217 .
   Web of Science ®Google Scholar
• Barles , G. , Buckdahn , R. , Pardoux , E. ( 1997 ). Backward stochastic differential equations and integral-partial differential equations . Stochastics Stochastics Rep. 60 : 57 – 83 .
   Google Scholar
• Barles , G. , Imbert , C. ( 2008 ). Second order elliptic integro-differential equations, Viscosity solutions theory revisited . Inst. H. Poincaré, Anal. Non Linéare 25 : 567 – 585 .
   Web of Science ®Google Scholar
• Bensoussan , A. , Lions , J. L. , Papanicolaou , G. ( 1978 ). Asymptotic Analysis for Periodic Structures . Amsterdam : North-Holland .
   Google Scholar
• Cont , R. , Tankov , P. ( 2003 ). Financial Modeling with Jump-Diffusion Processes . London : Chapman and Hall/CRC Press .
   Google Scholar
• Crandall , M. G. , Ishii , H. , Lions , P.-L . ( 1992 ). User's guide to viscosity solutions of second order partial differential equations . Bulletin of the AMS 27 : 1 – 67 .
   Web of Science ®Google Scholar
• Evans , L.C. ( 1992 ). Periodic homogeneization of certain fully nonlinear partial differential equations . Proc. Roy. Soc. Edinburgh A 120 : 245 – 265 .
   Google Scholar
• Fouque , J.-P. , Papanicolaou , G. , Sircar , K. R. ( 2000 ). Derivatives in Financial Markets with Stochastic Volatility . Cambridge : Cambridge University Press .
   Google Scholar
• Jacobsen , E. , Karlsen , K. ( 2006 ). A “Maximum principle for semicontinuous functions” applicable to integro-partial differential equations . Nodea Nonlinear Differential Equations Appl. 13 ( 2 ): 137 – 165 .
   Google Scholar
• Lions , P.-L. , Papanicolau , G. , Varadhan , S. R. S. Homogeneizations of Hamilton–Jacobi equations. Preprint.
   Google Scholar
• Pham , H. ( 1998 ). Optimal stopping of controlled jump diffusion processes: A viscosity solution approach . J. Math. Systems Estim. Control 8 ( 1 ): 27 .
   Google Scholar
• Sayah , A. ( 1991 ). Equations d'Hamilton-Jacobi du premiere ordre avec termes intégro-differentieles. I. Unicité des solutions de viscosité. II. Existence de solutions de viscosité [First order Hamilton–Jacobi equation with integro-differential terms. I. Uniqueness of the viscosity solutions. II. Existence of the viscosity solutions] . Comm. Partial Differential Equations 16 : 1057 – 1093 .
   Web of Science ®Google Scholar