The approximate Euler method for Lévy driven stochastic differential equations
Annales de l'I.H.P. Probabilités et statistiques, Tome 41 (2005) no. 3, pp. 523-558. 
@article{AIHPB_2005__41_3_523_0,
     author = {Jacod, Jean and Kurtz, Thomas G. and M\'el\'eard, Sylvie and Protter, Philip},
     title = {The approximate {Euler} method for {L\'evy} driven stochastic differential equations},
     journal = {Annales de l'I.H.P. Probabilit\'es et statistiques},
     pages = {523--558},
     publisher = {Elsevier},
     volume = {41},
     number = {3},
     year = {2005},
     doi = {10.1016/j.anihpb.2004.01.007},
     mrnumber = {2139032},
     zbl = {1071.60046},
     language = {en},
     url = {http://archive.numdam.org/articles/10.1016/j.anihpb.2004.01.007/}
}
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Jacod, Jean; Kurtz, Thomas G.; Méléard, Sylvie; Protter, Philip. The approximate Euler method for Lévy driven stochastic differential equations. Annales de l'I.H.P. Probabilités et statistiques, Tome 41 (2005) no. 3, pp. 523-558. doi : 10.1016/j.anihpb.2004.01.007. http://archive.numdam.org/articles/10.1016/j.anihpb.2004.01.007/

[1] S. Asmussen, J. Rosiński, Approximations of small jumps of Lévy processes with a view towards simulation, J. Appl. Probab. 38 (2001) 482-493. | MR | Zbl

[2] V. Bally, D. Talay, The law of the Euler scheme for stochastic differential equations (I): convergence rate of the distribution function, Probab. Theory Related Fields 104 (1996) 43-60. | MR | Zbl

[3] S.N. Ethier, M.F. Norman, Error estimate for the diffusion approximation of the Wright-Fisher model, Proc. Nat. Acad. Sci. USA 74 (11) (1977) 5096-5098. | MR | Zbl

[4] S.N. Ethier, T.G. Kurtz, Characterization and Convergence, Wiley, New York, 1986. | MR

[5] J. Jacod, P. Protter, Asymptotic error distributions for the Euler method for stochastic differential equations, Ann. Probab. 26 (1998) 267-307. | MR | Zbl

[6] J. Jacod, The Euler scheme for Lévy driven stochastic differential equations, Prépublication LPMS 711, 2002.

[7] J. Jacod, A.N. Shiryaev, Limit Theorems for Stochastic Processes, Springer-Verlag, Heidelberg, 2003. | MR | Zbl

[8] A. Kohatsu-Higa, N. Yoshida, On the simulation of some functionals of solutions of Lévy driven sde's, Preprint, 2001.

[9] T.G. Kurtz, P. Protter, Wong-Zakai corrections, random evolutions, and simulation schemes for SDEs, in: Mayer-Wolf E., Merzbach E., Shwartz A. (Eds.), Stochastic Analysis, Academic Press, Boston, MA, 1991, pp. 331-346. | MR | Zbl

[10] T.G. Kurtz, P. Protter, Weak error estimates for simulation schemes for SDEs, 1999.

[11] G.C. Papanicolaou, W. Kohler, Asymptotic theory of mixing stochastic ordinary differential equations, Comm. Pure Appl. Math. 27 (1974) 641-668. | MR | Zbl

[12] P. Protter, D. Talay, The Euler scheme for Lévy driven stochastic differential equations, Ann. Probab. 25 (1997) 393-423. | MR | Zbl

[13] J. Rosiński, Series representations of Lévy processes from the perspective of point processes, in: Barndorff-Nielsen O.E., Mikosch T., Resnick S.I. (Eds.), Lévy Processes - Theory and Applications, Birkhäuser, Boston, 2001, pp. 401-415. | MR | Zbl

[14] S. Rubenthaler, Numerical simulation of the solution of a stochastic differential equation driven by a Lévy process, Stochastic Process. Appl. 103 (2003) 311-349. | MR | Zbl

[15] L. Słominski, Stability of strong solutions of stochastic differential equations, Stochastic Process. Appl. 31 (1989) 173-202. | Zbl

[16] D. Talay, L. Tubaro, Expansion of the global error for numerical schemes solving stochastic differential equations, Stochastic Anal. Appl. 8 (1990) 94-120. | MR | Zbl

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