@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},
year = {2005},
publisher = {Elsevier},
volume = {41},
number = {3},
doi = {10.1016/j.anihpb.2004.01.007},
mrnumber = {2139032},
zbl = {1071.60046},
language = {en},
url = {https://www.numdam.org/articles/10.1016/j.anihpb.2004.01.007/}
}
TY - JOUR AU - Jacod, Jean AU - Kurtz, Thomas G. AU - Méléard, Sylvie AU - Protter, Philip TI - The approximate Euler method for Lévy driven stochastic differential equations JO - Annales de l'I.H.P. Probabilités et statistiques PY - 2005 SP - 523 EP - 558 VL - 41 IS - 3 PB - Elsevier UR - https://www.numdam.org/articles/10.1016/j.anihpb.2004.01.007/ DO - 10.1016/j.anihpb.2004.01.007 LA - en ID - AIHPB_2005__41_3_523_0 ER -
%0 Journal Article %A Jacod, Jean %A Kurtz, Thomas G. %A Méléard, Sylvie %A Protter, Philip %T The approximate Euler method for Lévy driven stochastic differential equations %J Annales de l'I.H.P. Probabilités et statistiques %D 2005 %P 523-558 %V 41 %N 3 %I Elsevier %U https://www.numdam.org/articles/10.1016/j.anihpb.2004.01.007/ %R 10.1016/j.anihpb.2004.01.007 %G en %F AIHPB_2005__41_3_523_0
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
[1] , , Approximations of small jumps of Lévy processes with a view towards simulation, J. Appl. Probab. 38 (2001) 482-493. | Zbl | MR
[2] , , 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. | Zbl | MR
[3] , , Error estimate for the diffusion approximation of the Wright-Fisher model, Proc. Nat. Acad. Sci. USA 74 (11) (1977) 5096-5098. | Zbl | MR
[4] , , Characterization and Convergence, Wiley, New York, 1986. | MR
[5] , , Asymptotic error distributions for the Euler method for stochastic differential equations, Ann. Probab. 26 (1998) 267-307. | Zbl | MR
[6] J. Jacod, The Euler scheme for Lévy driven stochastic differential equations, Prépublication LPMS 711, 2002.
[7] , , Limit Theorems for Stochastic Processes, Springer-Verlag, Heidelberg, 2003. | Zbl | MR
[8] A. Kohatsu-Higa, N. Yoshida, On the simulation of some functionals of solutions of Lévy driven sde's, Preprint, 2001.
[9] , , Wong-Zakai corrections, random evolutions, and simulation schemes for SDEs, in: , , (Eds.), Stochastic Analysis, Academic Press, Boston, MA, 1991, pp. 331-346. | Zbl | MR
[10] T.G. Kurtz, P. Protter, Weak error estimates for simulation schemes for SDEs, 1999.
[11] , , Asymptotic theory of mixing stochastic ordinary differential equations, Comm. Pure Appl. Math. 27 (1974) 641-668. | Zbl | MR
[12] , , The Euler scheme for Lévy driven stochastic differential equations, Ann. Probab. 25 (1997) 393-423. | Zbl | MR
[13] , Series representations of Lévy processes from the perspective of point processes, in: , , (Eds.), Lévy Processes - Theory and Applications, Birkhäuser, Boston, 2001, pp. 401-415. | Zbl | MR
[14] , Numerical simulation of the solution of a stochastic differential equation driven by a Lévy process, Stochastic Process. Appl. 103 (2003) 311-349. | Zbl | MR
[15] , Stability of strong solutions of stochastic differential equations, Stochastic Process. Appl. 31 (1989) 173-202. | Zbl
[16] , , Expansion of the global error for numerical schemes solving stochastic differential equations, Stochastic Anal. Appl. 8 (1990) 94-120. | Zbl | MR
Cité par Sources :






